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MATH 70 Course Overview
Algebra Review
354
Mathematics
Undergraduate 1
03/06/2012
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Term
Solution to a system of equations
 Definition
The pair of x- and y-coordinates that satisfy both equations
Term
The Substitution Method will
always/never/sometimes
work for solving a system of equations.
 Definition
Always
Term
The Graphing Method will
always/never/sometimes
work for solving a system of equations.
 Definition
Always
Term
When factoring trinomials, the first method to try is ______. After doing that, the next method to try is the ________.
 Definition
GCF; Box Method
Term
On you calculator, when a number has the E (i.e. 8.9456234E6), your calculator is providing an answer in _________ notation.
 Definition
scientific
Term
For a parabola, the range always begins at the ______.
 Definition
y-coordinate of the vertex
Term
PLANE
 Definition
A flat, two-dimensional surface extending forever in all dimensions (kind of like a super-huge piece of paper that goes on forever)
Term
On the TI calculator, to access the table press _______.
 Definition
Second and then Graph
Term
If the y-intercept of a line is -4 and the slope of the line is 6, the equation of the line is _____.
 Definition
y=6x-4 OR y=-4+6x
Term
For the equation y=4x+10, the slope can be written as a fraction. In that case it would be _____.
 Definition
4/1
Term
T/F: Similar triangles have angles that are the same size.
 Definition
True
Term
MEDIAN
 Definition
The middle number in a set of ordered numbers
Term
FACTOR (n.)
 Definition
Things that are multiplied together (i.e. In the term 4yz, 4, y, and z are the three factors of the term)
Term
T/F: Division by 0 is okay.
 Definition
FALSE (i.e. 4/0, -6/0)
Term
When subtracting 2 numbers that have the same sign, the answer will be positive always/never/sometimes.
 Definition
Sometimes (i.e. 3-2=+1 but -3-(-2)=-1
Term
T/F: The following terms are NOT like terms.
3xyz, -2.5yzx
 Definition
False, they have the same variables
Term
PER means _____.
 Definition
Divide
Term
PERIMETER
 Definition
The sum of all sides (i.e. the distance around an object or shape)
Term
AREA
 Definition
How much space there is on a surface (i.e. how much space on a wall or on a table)
Term
MEAN
 Definition
The average of a set of numbers.
Term
Calculate the MEAN
 Definition
Add up all numbers in the problem and divide by how many you added together
Term
Calculate the MEDIAN
 Definition
Put the numbers in order and if there's an odd number of numbers, the middle number is the median. Otherwise, take the two numbers that are in the middle and find their mean.
Term
LIKE TERMS
 Definition
Terms that have the EXACT same collection of variables
Term
LCD
 Definition
Least Common Denominator (the LCM of the denominators)
Term
LCM
 Definition
Least Common Multiple
Term
Coefficient
 Definition
The number that is multiplied by a variable (i.e. 3 is the coefficient of 3x)
Term
RECIPROCAL
 Definition
The result of flipping a fraction (i.e. the reciprocal of 2/3 is 3/2)
Term
TERM (MONOMIAL)
 Definition
A collections of numbers and/or variables that are multiplied together (i.e. 3x + 4yz, 3x and 4yz are separate terms)
Term
MONOMIAL
 Definition
A single term (i.e., 3x, 4y, 8qw)
Term
BINOMIAL
 Definition
Two terms (i.e. 4x+7y, -9h+6R)
Term
TRINOMIAL
 Definition
Three terms (i.e. -3D-5J+4, 2x+3y+6L)
Term
T/F: 0 divided by anything is 0.
 Definition
TRUE (i.e. 0/3, 0/(-8))
Term
When dividing by a fraction you must ________.
 Definition
First flip the second fraction (get its reciprocal) and then change the division to multiplication.
Term
ORDER OF OPERATIONS
 Definition
PEMDAS
Parentheses
Exponents
Multiplications & Divisions
Additions & Subtractions
Term
In simplifying an expression, you always do it from ______ to ______.
 Definition
Left, Right
Term
EXPRESSION
 Definition
Something WITHOUT an equal sign
Term
EQUATION
 Definition
Something WITH an equal sign
Term
When multiplying 2 numbers that have the same sign (both positive OR both negative) the answer will be _______.
 Definition
Positive
Term
When multiplying 2 numbers that have different signs (one positive and one negative) the answer will be _______.
 Definition
Negative
Term
When dividing 2 numbers that have the same sign (both positive OR both negative) the answer will be _______.
 Definition
Positive
Term
When dividing 2 numbers that have different signs (one positive and one negative) the answer will be _______.
 Definition
Negative
Term
When adding 2 numbers that have the same sign, the answer will be positive always/never/sometimes.
 Definition
Sometimes (i.e.3+6=+9 but -3+(-6)=-9)
Term
T/F: -9+(-5)=-4
 Definition
False, the answer is -14
Term
T/F: -13-28=15 or -15
 Definition
False, the answer is -41
Term
T/F: The square root of -16 has no real number solution
 Definition
True, negative numbers do not have real number square roots
Term
How many terms are in the expression?
-2x+3y-4xyz
 Definition
3, Remember that addition and subtraction separate terms.
Term
NUMERATOR
 Definition
The top of a fraction
Term
DENOMINATOR
 Definition
The bottom of a fraction
Term
Before you cancel a factor out of the top and the bottom of an algebraic expression, you must first be able to _________.
 Definition
FACTOR out of the top and the bottom whatever it is you wish to cancel.
Term
When dividing by a fraction you must _________ the ________ fraction.
 Definition
Flip (get the reciprocal), Second
Term
The only time you can cancel a factor between a pair of fractions is when the two fractions are being ___________.
 Definition
Multiplied
Term
DEGREE OF A TERM (Monomial)
 Definition
The sum of the exponents on the variables (i.e. -4xyz has degree 3, 15xQ^5 has degree 6)
Term
DEGREE OF A POLYNOMIAL
 Definition
Find the degree of each term and whichever one is the biggest is the degree of the entire polynomial.
Term
When you add or subtract, you must have _________.
 Definition
Like Terms
Term
When you add or subtract fractions, you must have ___________.
 Definition
Common denominators AND like terms
Term
T/F: The sign in front of a number (just to the left of it) stays with that number.
 Definition
True
Term
PRIME NUMBER
 Definition
A number that can only be divided by 1 and itself.
Term
COMPOSITE NUMBER
 Definition
A number that can be divided by at least 1 other integer besides 1 and itself
Term
INTEGER
 Definition
A number in the following set:
...,-3,-2,-1,0,1,2,3,...
Term
GCF
 Definition
Greatest Common Factor
Term
GREATEST COMMON FACTOR
 Definition
The largest integer that divides into both numbers (i.e. The GCF of 16 and 24 is 8)
Term
LEAST COMMON MULTIPLE
 Definition
The smallest integer that both numbers divide into (i.e. The LCM of 6 and 16 is 32)
Term
VOLUME
 Definition
How much room there is inside of something (i.e. inside a box or a freezer)
Term
When plugging a number into an expression, it's a good idea to put ________ around the number.
 Definition
Parentheses
Term
LINEAR EXPRESSION
 Definition
An expression whose highest power of x is 1
Term
"Twenty less than a number" translates into___________.
 Definition
x-20 (NOTE: The answer is NOT 20-x)
Term
COMPLIMENTARY ANGLES
 Definition
Angles that add up to 90 degrees
Term
SUPPLEMENTARY ANGLES
 Definition
Angles that add up to 180 degrees
Term
The angles of a triangle always add up to _______.
 Definition
180 degrees
Term
When doing operations on mixed numbers it is a good idea to first _________.
 Definition
Convert all mixed numbers to improper fractions
Term
T/F: When evaluating the square root of a fraction you MUST first rewrite the problem as the square root of the numerator divided by the square root of the denominator.
 Definition
False, you can do that but you don't have to
Term
ORIGIN
 Definition
Where the x-axis and y-axis intersect
Term
The coordinates of the origin are _____.
 Definition
(0,0)
Term
FUNCTION
 Definition
A rule wherein x-values are NOT repeated (used more than once)
Term
DOMAIN
 Definition
All the numbers that when plugged into a function for x, yield an answer
Term
RANGE
 Definition
All the y-values that a function uses
Term
X-INTERCEPT
 Definition
Where the graph of a function intersects (touches) the x-axis.
Term
To find the x-intercept of a function you must _________.
 Definition
set y = 0 and then solve
Term
Y-INTERCEPT
 Definition
Where the graph of a function intersects (touches) the y-axis.
Term
To find the y-intercept of a function you must _________.
 Definition
set x = 0 and then solve
Term
Why do I set x=0 to find the y-intercept of a function?
 Definition
Because y-intercepts are on the y-axis and every point on the y-axis has an x-coordinate = 0
Term
Why do I set y=0 to find the x-intercepts of a function?
 Definition
Because x-intercepts are on the x-axis and every point on the x-axis has a y-coordinate = 0
Term
ACUTE ANGLE
 Definition
Angle that is less than 90 degrees
Term
OBTUSE ANGLE
 Definition
Angle that is more than 90 degrees
Term
RIGHT ANGLE
 Definition
A 90 degree angle (i.e. like the angle formed where the wall and the floor meet)
Term
POINT
 Definition
A single dot on a graph
Term
LINE
 Definition
A straight, one-dimensional figure extending forever in BOTH directions
Term
RAY
 Definition
A straight, one-dimensional figure extending forever in one direction from a single point; in other words, half a line
Term
PARALLEL LINES
 Definition
Lines that never touch
Term
CONGRUENT ANGLES
 Definition
Angles that have the same measure (are equal)
Term
PERPENDICULAR LINES
 Definition
Lines that meet at a right angle (like the crossbeams of a standard kite)
Term
RIGHT TRIANGLE
 Definition
A triangle with ONE right angle
Term
ACUTE TRIANGLE
 Definition
A triangle with THREE acute angles
Term
OBTUSE TRIANGLE
 Definition
A triangle with ONE obtuse angle
Term
EQUILATERAL TRIANGLE
 Definition
A triangle with all sides equal and all angles equal (in this case the angles will all be 60 degrees)
Term
On the coordinate plane, the first quadrant is found in the ________corner.
 Definition
Upper Right
Term
On the coordinate plane, the second quadrant is found in the ________corner.
 Definition
Upper Left
Term
On the coordinate plane, the third quadrant is found in the ________corner.
 Definition
Lower Left
Term
On the coordinate plane, the fourth quadrant is found in the ________corner.
 Definition
Lower right
Term
When converting a fraction to a decimal, divide the _______ by the ________.
 Definition
Numerator, Denominator
Term
To compare fractions to see which one is bigger you can either _______ or _______.
 Definition
Get common denominators, Convert both fractions to decimals
Term
To change a percent to a decimal, you must move the decimal point ______.
 Definition
To the left 2 places
Term
To change a decimal to a percent, you must move the decimal point ______.
 Definition
To the right 2 places
Term
To enter a function into the calculator you must press the button labeled _____.
 Definition
Y=
Term
(3,0) is a ___-intercept.
 Definition
X
Term
(-7,0) is a ___-intercept
 Definition
X
Term
(0,5) is a ___-intercept
 Definition
Y
Term
(0,-8) is a ___-intercept
 Definition
Y
Term
For a linear equation, when Y is by itself, we say that the equation is in __________ form.
 Definition
Slope-intercept
Term
For a linear equation, when Y is by itself, we say that the equation is in __________ form.
 Definition
Slope-intercept
Term
In a linear equation, when Y is by itself, the slope is ALWAYS the number _________ by x.
 Definition
Multiplied
Term
In a linear equation, when Y is by itself, the Y-intercept is ALWAYS the number _________ to x.
 Definition
Added
Term
A handy way to remember slope is _______ over _______.
 Definition
Rise, Run
Term
When we say "slope is rise over run" the 'rise' means the difference in the __________ from one point to another.
 Definition
Y-values
Term
When we say "slope is rise over run" the 'run' means the difference in the __________ from one point to another.
 Definition
X-Values
Term
T/F: In the expression -7-9, the two negatives can both be changed to positives.
 Definition
False, in order to be able to change them both to positives, they have to be right next to each other.
Term
T/F: In the expression -(-9), the two negatives can both be changed to positives.
 Definition
True
Term
T/F: If a fraction is negative, it doesn't matter if the negative is applied to the NUMERATOR or the DENOMINATOR or in front of the fraction.
 Definition
True
Term
INPUT
 Definition
What you plug into a function for x
Term
OUTPUT
 Definition
The result after you plug in a number for x into a function
Term
X-AXIS
 Definition
The horizontal axis of a graph
Term
Y-AXIS
 Definition
The vertical axis of a graph
Term
T/F: Addition is commutative
 Definition
TRUE (i.e. 3+2=2+3)
Term
T/F: Subtraction is commutative
 Definition
False (i.e. 2-3 does not equal 3-2)
Term
T/F: Multiplication is commutative
 Definition
True (i.e. 3*2=2*3)
Term
T/F: Division is commutative
 Definition
False (i.e. 2/3 does not equal 3/2)
Term
If a variable does not appear to be multiplied by a number, then its coefficient is ____.
 Definition
1
Term
When multiplying 2 things together, you may add their exponents only when _________.
 Definition
The bases of the exponents are the same (i.e. x^2*x^3=x^5)
Term
The only time you ever multiply 2 exponents by each other is when ______.
 Definition
One exponent is raised to the power of another (i.e. (x^2)^3=x^6)
Term
Cubic inches are used for measuring ________.
 Definition
Volume
Term
Cubic feet are used for measuring ________.
 Definition
Volume
Term
Cubic meters are used for measuring ________.
 Definition
Volume
Term
Square inches are used for measuring ________.
 Definition
Area
Term
Square feet are used for measuring ________.
 Definition
Area
Term
Square meters are used for measuring ________.
 Definition
Area
Term
Another way to write 3
 Definition
(3,7)
Term
Another way to write -4<=x<9 is____.
 Definition
[-4,9)
Term
Another way to write x>8 is ______.
 Definition
(8,infinity)
Term
If the equation for renting a jackhammer is y=35x+50, the 50 probably means ________.
 Definition
The initial rental fee (up front).
Term
If the equation for renting a jackhammer is y=35x+50, the 35 probably means ________.
 Definition
The hourly cost
Term
If an equation begins as:
3x-11=7
and changes to become:
3x=18,
what happened?
 Definition
Eleven was added to both sides
Term
After solving an equation for the given variable, a way to check your work is to ____________.
 Definition
Plug your solution into the ORIGINAL problem for the variable and make sure both sides of the equation are equal.
Term
If you have a function f(x)=3x-7, then f(5) means _______.
 Definition
The y-value that is paired up with the x-value, 5.
Term
If you have a function g(x)=8-6x, then g(-3) means _______.
 Definition
The y-value that is paired up with the x-value, -3.
Term
On the TI calculator, to access the graph press _______.
 Definition
Graph
Term
On the TI calculator, to access the table setup screen, press _______.
 Definition
Second and then Window
Term
On the Table Setup screen on the TI calculator, the first number tells you _______.
 Definition
What will be the first x-value displayed on your Table
Term
On the Table Setup screen on the TI calculator, the second number tells you _______.
 Definition
What your x-values will increase by on the Table
Term
The best way to solve 3x-8=4 is to first move the ____ to the other side of the equation then move the _____.
 Definition
8, 3
Term
When you see the phrase "in terms of", the variable that comes directly before the phrase is the ________ variable.
 Definition
Dependent
Term
When you see the phrase "in terms of", the variable that comes directly after the phrase is the ________ variable.
 Definition
Independent
Term
To solve the equation:
PV=nRT for the variable R, you would need to ________ both sides of the equation by _____.
 Definition
Divide, nT
Term
To solve the equation:
A=3r^2
for the variable r, you would need to ________ both sides of the equation by _____ and then ______ of both sides.
 Definition
Divide, 3, take the square root
Term
If a relation passes the Vertical Line Test, ________.
 Definition
It is a function
Term
If a relation doesn't pass the Vertical Line Test, ________.
 Definition
It is not a function
Term
If a relation uses a value for x more than once, ________.
 Definition
It is not a function
Term
If a relation uses a value for y more than once, it ____ a function.
 Definition
May or may not be a function (how often the y-values get uses has no bearing on whether or not it is a function-only if you use an x-value more than once)
Term
T/F: The relation
(1,6),(2,6),(3,6),(4,6)
is a function.
 Definition
True
Term
T/F: The relation
(6,1),(6,2),(6,3),(6,4)
is a function.
 Definition
False
Term
Like a book, graphs are read from _____ to _____.
 Definition
Left, Right
Term
If the graph of a line goes down, from left to right, it has a ____ slope.
 Definition
Negative
Term
If the graph of a line goes up, from left to right, it has a ____ slope.
 Definition
Positive
Term
If the graph of a line is flat (horizontal), from left to right, it has a ____ slope.
 Definition
0
Term
X-intercepts of functions are found by setting ____ equal to _____ and then solving.
 Definition
Y,0
Term
Y-intercepts of functions are found by setting ____ equal to _____ and then solving.
 Definition
X,0
Term
When the equation of a line is in slope-intercept form, the number multiplied by X is the ____.
 Definition
Slope
Term
When the equation of a line is in slope-intercept form, the number added to X is the ____.
 Definition
Y-intercept
Term
Slope is represented by the variable ____.
 Definition
M
Term
Y-intercepts are represented by the variable ___.
 Definition
B
Term
When the equation of a line is in slope-intercept form, _______.
 Definition
Y is by itself/isolated.
Term
The slope of the equation y=3x-9 is ____.
 Definition
3
Term
The y-intercept of the equation y=3x-9 is ____.
 Definition
-9
Term
The slope of the equation y=3-9x is ____.
 Definition
-9
Term
The y-intercept of the equation y=3-9x is ____.
 Definition
3
Term
Two lines are parallel if their slopes are _____ AND if their y-intercepts are _____.
 Definition
Equal, Different
Term
Two lines are perpendicular if their slopes _____.
 Definition
Multiply to -1
Term
A 'proportion' is ________.
 Definition
A single fraction equal to a single fraction (i.e. 3/x = 2/5)
Term
There are _____ centimeters in a meter.
 Definition
100
Term
There are _____ meters in a kilometer.
 Definition
1000
Term
There are _____ millimeters in a centimeter.
 Definition
10
Term
There are about _____ centimeters in an inch.
 Definition
2.5
Term
T/F: Similar triangles have sides that are the same lengths.
 Definition
False, (rather they are proportional to each other)
Term
System of Equations
 Definition
A group of 2 or more equations
Term
Solution to a system of equations
 Definition
The point(s) at which the graphs of the 2 equations intersect
Term
Parallel Lines
 Definition
Equations that have the SAME slope and DIFFERENT y-intercepts
Term
Coincident Lines
 Definition
Equations that are the same (more easily viewed when you solve for y in both equations)
Term
Coincident Equations have ______ solutions.
 Definition
infinitely many
Term
In solving a word problem, always set the variable equal to __________.
 Definition
whatever you're asked to solve for
Term
A good way to start any word problem is to __________.
 Definition
define your variables (i.e. x=number of bananas/crate; y=number of pounds of bananas/crate)
Term
The first step of the Substitution Method for solving a system of equations is to __________.
 Definition
isolate either of the variables in either equation
Term
Choose One of the Three Choices.
The Elimination Method will
always/never/sometimes
work for solving a system of equations.
 Definition
Always
Term
When solving a system of equations using the Elimination Method, you must always first make certain that both equations ____________.
 Definition
have all terms lined up (i.e. x-terms above x-terms, y-terms above y-terms, etc.)
Term
When graphing linear inequalities, use a dotted line when there is ___________.
 Definition
a "less than" or "greater than" sign
Term
When graphing linear inequalities, use a solid line when there is ___________.
 Definition
a "less than or equal to" or "greater than or equal to" sign
Term
When a linear inequality is of the form y
 Definition
below
Term
When a linear inequality is of the form y>mx+b, shade ________ the line.
 Definition
above
Term
When multiplying polynomials you must multiply each _________ in the first polynomial with each _________ of the second polynomial.
 Definition
term; term
Term
When factoring polynomials, the first factoring technique to try is always ______.
 Definition
GCF
Term
When factoring a quadratic binomial, it can sometimes be helpful to try using the _________method.
 Definition
Difference of Squares.
Term
Factors
 Definition
Numbers and variables that are MULTIPLIED together
Term
Terms
 Definition
Numbers and variables that are ADDED together
Term
True or False:
When factoring a binomial using the Difference of Squares method, you MUST write the '-' term first and the '+' term second. (i.e.x^2-9=(x-3)(x+3) but x^2-9does not=(x+3)(x-3)
 Definition
False
Term
True or False:
As a student, it would be a SUPREMELY good idea to learn how to factor polynomials right away and not "wing it" through MATH 65 and on into MATH 70.
 Definition
True
Term
When factoring the polynomial:
3x^2+12x+9
the first factoring technique to be attempted should be ______. The second method to be attempted is _________.
 Definition
GCF; the Box Method
Term
When you have an expression in which there is a 'power to a power' (i.e. (3^2)^5) you should ________ the powers.
 Definition
multiply
Term
When you have an expression in which you are multiplying two powers and the bases of the exponents are the same (i.e. 4^5*4^8), you should _________ the exponents.
 Definition
add
Term
When you have an expression in which you are dividing two powers and the bases of the exponents are the same (i.e. 4^5/4^8), you should _________ the exponents.
 Definition
subtract
Term
Anything (except 0) raised to the power of 0 is equal to ____.
 Definition
1
Term
True or False:
Negative exponents make the whole problem negative.
 Definition
False, a negative sign in an exponent has NOTHING TO DO WITH THE SIGN OF THE ANSWER.
Term
When switching from a negative exponent to a positive exponent (or visa versa), this will cause the expression to _______.
 Definition
be flipped (i.e. (2/3)^-4 = (3/2)^4
Term
When switching from a positive exponent to a negative exponent (or visa versa), this will cause the expression to _______.
 Definition
be flipped (i.e. (2/3)^4 = (3/2)^-4
Term
In a right triangle, the _______ is always the longest side.
 Definition
hypotenuse
Term
In a right triangle, the 2 sides that form the right angle are called the _____ of the right triangle.
 Definition
legs
Term
True or False:
In a right triangle, the hypotenuse is one of the sides that helps form the right angle.
 Definition
False, the hypotenuse NEVER helps form the right angle
Term
The square root of a number(or variable) is the same as that number raised to the ____ power.
 Definition
1/2
Term
When you square the square-root of a number, your answer is always ________.
 Definition
that number
Term
A radicand is what is ________ a radical sign.
 Definition
inside
Term
In the Real Numbers, a radicand must always be:
(a) greater than zero
(b) greater than or equal to zero
(c) less than zero
 Definition
b
Term
When solving a radical equation, begin by doing what to both sides of the equation.
 Definition
squaring
Term
To determine the x-intercepts of a function, we replace y with 0 and then solve. The reason is because ________.
 Definition
x-intercepts are always on the x-axis and therefore always have a y-coordinate of 0
Term
To determine the y-intercept of a function, we replace x with 0 and then solve. The reason is because ________.
 Definition
y-intercepts are always on the y-axis and therefore always have an x-coordinate of 0
Term
For a parabola, the Axis of Symmetry always goes through ______.
 Definition
the vertex of the parabola
Term
For a parabola, the Axis of Symmetry is always a ______ line.
 Definition
vertical
Term
For a parabola, the equation of the Axis of Symmetry is always ___ = ____.
 Definition
x; x-coordinate of vertex
Term
True or False:
For a parabola, the vertex is always the maximum point on the graph.
 Definition
False; sometimes that's true, but when it isn't, the vertex will be the minimum point of the graph
Term
When solving for a variable in an equation, if you have to take the square root of both sides, you MUST then _____.
 Definition
assign a '+ or -' to the solution
Term
In a polynomial equation, if you use factoring to solve it, you consequently set each factor equal to _____ and then solve _______.
 Definition
0; both equations
Term
When solving a system of equations, if you end up with an obviously false statement (i.e. 3=7), this is called a ________ and means ________.
 Definition
contradiction; there is no solution to the system of equations
Term
When solving a system of equations, if you end up with an obviously true statement (i.e. 5=5), this is called an ________ and means ________.
 Definition
identity; there are infinitely many solutions since the two equations are the same thing
Term
The Quadratic Formula will solve _____ quadratic equations.
(a) some
(b) none
(c) all
 Definition
c
Term
The radicand of the Quadratic Equation is called the _________.
 Definition
discriminant
Term
If the Discriminant is positive, this means _________.
 Definition
there are 2 real-number solutions
Term
If the Discriminant is negative, this means _________.
 Definition
there are no real-number solutions
Term
If the Discriminant is zero, this means _________.
 Definition
there is exactly 1 real-number solution
Term
A rational function is a function that can be expressed as a ______ and the denominator contains _______.
 Definition
fraction; variables
Term
The denominator of a fraction can never equal _____.
 Definition
zero
Term
For the function:
f(x) = 3/(x-4)
the domain is _______.
 Definition
All numbers except 4 since plugging 4 in for x would cause the denominator to be zero.
Term
For the function:
f(x) = -7x/(x+3)
the domain is _______.
 Definition
All numbers except -3 since plugging -3 in for x would cause the denominator to be zero.
Term
For the function:
f(x) = 19.5x/(2x-6)
the domain is _______.
 Definition
All numbers except 3 since plugging 3 in for x would cause the denominator to be zero.
Term
For the function:
f(x) = 8x/(5+2x)
the domain is _______.
 Definition
All numbers except -2.5 since plugging -2.5 in for x would cause the denominator to be zero.
Term
For the function:
f(x) = 3/(x^2-4)
the domain is _______.
 Definition
All numbers except 2 or -2 since plugging 2 or -2 in for x would cause the denominator to be zero.
Term
When simplifying a rational expression, the first step is ALWAYS to ________ all numerators and denominators.
 Definition
factor
Term
When getting common denominators for a pair of fractions, you always have to multiply the numerator and denominator of each individual fraction by the same thing. Why?
 Definition
So that, in effect, you are multiplying by the number 1. Therefore you're not changing the value of the fraction.
Term
One way to rewrite the expression (2x-3) is to write it as _______.
 Definition
-1(3-2x)
Term
One way to rewrite the expression (4x-7) is to write it as _______.
 Definition
-1(7-4x)
Term
One way to rewrite the expression (x-10) is to write it as _______.
 Definition
-1(10-x)
Term
When solving a rational equation, you should start by _______ both sides of the equation by the _____. This will ________.
 Definition
multiplying; LCD; get rid of all denominators (fractions)
Term
An assumption is ____________.
 Definition
something not stated but taken as fact (i.e. Without reading the textbook, I will assume that it is accurate.)
Term
A condition is ____________.
 Definition
a requirement or restriction (i.e. A condition for graduation is passing MATH 111.)
Term
The word 'difference' means _______.
 Definition
subtraction
Term
The word 'sum' means _______.
 Definition
addition
Term
The word 'quotient' means _______.
 Definition
division
Term
The word 'product' means _______.
 Definition
multiplication
Term
In word problems, the word 'of' usually means ______.
 Definition
multiplication
Term
In the Order of Operations (PEMDAS), the P stands for ________.
 Definition
parentheses and all other grouping symbols (i.e. parentheses, brackets, braces, absolute values, square roots)
Term
In the Order of Operations (PEMDAS), the E stands for ________.
 Definition
exponents
Term
In the Order of Operations (PEMDAS), the M stands for ________.
 Definition
multiplication
Term
In the Order of Operations (PEMDAS), the D stands for ________.
 Definition
division
Term
In the Order of Operations (PEMDAS), the A stands for ________.
 Definition
addition
Term
In the Order of Operations (PEMDAS), the S stands for ________.
 Definition
subtraction
Term
When using the Order of Operations (PEMDAS) to simplify an expression, we simplify multiplications and divisions SIMULTANEOUSLY FROM _________.
 Definition
left to right
Term
When using the Order of Operations (PEMDAS) to simplify an expression, we simplify additions and subtractions SIMULTANEOUSLY FROM _________.
 Definition
left to right
Term
The 'input variable' is usually the variable ___.
 Definition
x
Term
The 'output variable' is usually the variable ___.
 Definition
y
Term
The 'independent variable' is usually the variable ___.
 Definition
x
Term
The 'dependent variable' is usually the variable ___.
 Definition
y
Term
T/F:
Pi is a variable.
 Definition
False, it doesn't vary. It's a constant. It's always the same number, 3.14159...
Term
When adding or subtracting, you must have ___________.
 Definition
like terms.
Term
When adding or subtracting fractions, you must have ___________.
 Definition
common denominators
Term
T/F:
"Five less than the input" translates to:
5-x
 Definition
False; it would translate to x-5
Term
The 'initial value' of a function is the function's _______.
 Definition
y-intercept (when x = 0)
Term
When solving an equation for x, you can ALWAYS __________.
 Definition
set the left side of the equation to y1, set the right side of the equation to y2, and see where they intersect!
Term
An 'identity' is ___________.
 Definition
something you can steal (just kidding),it's a statement that is obviously true (i.e. 3=3)
Term
A 'contradiction' is _________.
 Definition
a statment that is obviously false (i.e., 5=7)
Term
When you flip a fraction, you are finding the ___________.
 Definition
reciprocal
Term
Three main ways to write out the solution set to an inequality statement are: ______, ______, and ________.
 Definition
inequality notation; interval notation; line graph
Term
When graphing a function on the calculator, you must first enter the function on the menu labeled ______.
 Definition
y= (i.e., top lefthand button on the calculator)
Term
When graphing a function on the calculator, it is sometimes helpful to allow the calculator to select your ymin and ymax. To do this you must press _________.
 Definition
Zoom 0
Term
When graphing a collection of individual points on the calculator, the easiest way to select an approrpiate viewing window is to press Zoom ______.
 Definition
9
Term
To find the intersection point(s) of two functions, you enter the functions on the ______ menu, make sure the two functions appear on the screen when you graph, then press ___, ___, ___, ___, ___, ___.
 Definition
y=; Second; Trace; 5; Enter; Enter; Enter
Term
To enter individual points into the calculator you must press ____ and then _____.
 Definition
Stat; Enter
Term
To clear out a list of data (i.e., L1, L2,...), one way is to go to the lists, highlight the name of the list you wish to clear out and then press ____ and then _____.
 Definition
Clear; Enter
Term
To find the Line of Regression (i.e. Line of Best Fit), you enter your data with x-values in ____ and y-values in ____. Then, you would press ____, ____, ____, and _____ 5 times.
 Definition
L1; L2; Stat; Right Arrow; 4; Enter
Term
To generate an input-output table on the calculator, you must first enter the function on the _____ menu and then press _____ and then ______.
 Definition
y=; Second; Graph
Term
When graphing a function, usually it is easiest to select an appropriate viewing widow by pressing Zoom ____.
 Definition
6
Term
To find the maximum value of a function using the calculator, you would go to Second Trace and select _______.
 Definition
Maximum
Term
To find the minimum value of a function using the calculator, you would go to Second Trace and select _______.
 Definition
Minimum
Term
When plotting individual points on the calculator you must first go to the y= menu and turn on _______.
 Definition
Plot1
Term
On the calculator, the Absolute Value function is found by pressing _____, ______, _______.
 Definition
Math; Right Arrow; Enter
Term
On the calculator, the Inequality Symbols are found by pressing _____, ______.
 Definition
Second; Math
Term
When making a Line Graph to express an interval, a ___________ means you do NOT include that particular number in your solution.
 Definition
open circle
Term
When making a Line Graph to express an interval, a ___________ means you DO include that particular number in your solution.
 Definition
closed circle (i.e., a circle that is shaded in)
Term
In Interval Notation, parentheses are the same as _______ circles on a line graph.
 Definition
open
Term
In Interval Notation, brackets (i.e., [,] )are the same as _______ circles on a line graph.
 Definition
closed
Term
The symbol for inifinity looks like the number ___ laying down on its side.
 Definition
8
Term
In Interval Notation, infinity ALWAYS gets a _________ next to it.
 Definition
parentheses
Term
T/F:
In a function, each x-value can be used one time, at most.
 Definition
True
Term
T/F:
In a function, each y-value can be used one time, at most.
 Definition
False
Term
For the function f(x)=5x-7, f(2)=____.
 Definition
3
Term
For the function f(x)=5x-7, f(-3)=____.
 Definition
-22
Term
For the function f(x)=5x-7, f(Q)=____.
 Definition
5Q-7
Term
For the function f(x)=5x-7, f(R+W)=____.
 Definition
5(R+W)-7 (NOTE: this can be simplified using the Distributive Property)
Term
In word problems that use the variable TIME, this variable is usually the label for the _______ axis.
 Definition
horizontal
Term
If a function can be written in slope-intercept form, this means that _____________.
 Definition
the function is linear
Term
If a function can be written in slope-intercept form, this means that _____________.
 Definition
the function has a y-intercept
Term
If a function can be written in slope-intercept form, this means that _____________.
 Definition
the function has a CONSTANT slope
Term
The units for the slope of a function are always the ______ divided by the ______.
 Definition
units for y; units for x (i.e., if x is time measured in hours and y is distance measured in miles, then the units of slope will me 'miles/hour'.)
Term
To find the slope of a line that passes through 2 given points, we would use the formula ________.
 Definition
(y2-y1)/(x2-x1)
Term
If a function can be written in slope-intercept form, this means that _____________.
 Definition
it's graph is a straight line
Term
If a function has a slope of 0, this means its graph is a _______ line.
 Definition
horizontal
Term
If the graph of an equation is a vertical line, then its slope is _________.
 Definition
Undefined
Term
T/F:
If two lines have the same slope they are guaranteed to be parallel.
 Definition
False; they must also have the added condition of 'different y-intercepts'
Term
T/F:
Perpendicular lines sometimes have slopes that are the same sign.
 Definition
False; their slopes are ALWAYS oppositely signed (i.e., 2/3 and -3/2; -4/5 and 5/4; -17 and 1/17)
Term
T/F:
If two lines are perpendicular, then their slopes multiply to give -1.
 Definition
True (the only except is when considering a vertical line and a horizontal line)
Term
On the calculator, when calculating the Line of Best Fit/Regression Line (using LinReg), the value for 'r' that the calculator gives you tells you ______.
 Definition
how good of a fit the Line of Best Fit is for your data points that you entered
Term
T/F:
If a function passes through the origin, then we know the y-intercept and an x-intercept.
 Definition
True; both would be 0
Term
A constant function has slope equal to _____.
 Definition
0
Term
A constant function only has one variable in the equation: ______.
 Definition
y
Term
T/F:
The equation x=3 is a constant function.
 Definition
False; it's not a function (it doesn't pass the vertical line test), therefore it's not ANY kind of function!
Term
In math the word 'rate' basically means _____.
 Definition
slope
Term
In math the phrase'rate of change' basically means _____.
 Definition
slope
Term
In math, the word 'rational' basically means _______.
 Definition
Fraction; after all, the first 5 letters of the word 'rational' form the word 'ratio'
Term
To write y in terms of x means to solve for ____.
 Definition
y
Term
To write x in terms of y means to solve for ____.
 Definition
x
Term
To write Q in terms of P means to solve for ____.
 Definition
Q
Term
To write P in terms of Q means to solve for ____.
 Definition
P
Term
When solving a system of equations, the Substitution Method will work always/never/sometimes.
 Definition
Always
Term
When solving a system of equations, the Elimination Method will work always/never/sometimes.
 Definition
Always
Term
When solving a system of equations, the Graphing Method will work always/never/sometimes.
 Definition
Always
Term
To solve a system of equations by Graphing, you must first __________ in both equations.
 Definition
isolate y (that way you can plug the equations into your calculator on the 'y=' menu)
Term
In Quantity/Rate problems, a key word for numbers that are rates is ______.
 Definition
per (whenever you see 'per', you know the number is a 'rate')
Term
In Quantity/Rate problems, the first thing to do is define _________.
 Definition
the categories (i.e. Indonesian Coffee & Honduran Coffee; An account that pays 5% interest & an account that pays 3%)
Term
In Quantity/Rate tables, you ______ horizontally.
 Definition
multiply
Term
In Quantity/Rate tables, you ______ vertically.
 Definition
add (the exception is the 'rate' column)
Term
In Quantity/Rate tables, the last entry in the 'rate' column will always be greater/smaller/between the other rates listed above.
 Definition
between (this is the average rate for the problem)
Term
A quadratic function or equation is one in which the highest power of x is ___.
 Definition
2
Term
A linear function or equation is one in which the highest power of x is ___.
 Definition
1
Term
A cubic function or equation is one in which the highest power of x is ___.
 Definition
3
Term
A parabola is what you get when you graph a __________ function.
 Definition
quadratic
Term
A straight line is what you get when you graph a __________ function.
 Definition
linear
Term
x-intercepts are found by setting ___ equal to zero.
 Definition
y
Term
y-intercepts are found by setting ___ equal to zero.
 Definition
x
Term
The axis of symmetry of a parabola is the _______ line that passes through its _________.
 Definition
vertical; vertex
Term
The coordinates of the vertex of a parabola are denoted by the variables _____.
 Definition
(h,k)
Term
For a quadratic function opening up, the range is always ________.
 Definition
y greater than or equal to k (the y-coordinate of the vertex)
Term
If a quadratic function opened up (vertex is a minimum point) and the vertex is (3,4), then the range would be_______.
 Definition
y greater than or equal to 4.
Term
For a quadratic function opening down, the range is always ________.
 Definition
y less than or equal to k (the y-coordinate of the vertex)
Term
If a quadratic function opened down (vertex is a maximum point) and the vertex is (3,4), then the range would be_______.
 Definition
y less than or equal to 4.
Term
For quadratic functions, the domain is sometimes/always/never all real numbers.
 Definition
always
Term
When factoring a polynomial, the first factoring technique to try is always_______.
 Definition
GCF (i.e., for the polynomial 2x^2-4x+2, first factor out the GCF of 2, then try doing something else).
Term
When Completing The Square, the quantity that you add to both sides, so that the left side factors nicely, is _______.
 Definition
(b/2)^2 (NOTE: the b used here is not necessarily the b from the original problem; the b used here is the coefficient of x AFTER dividing both sides of the equation by a, the coefficient of x^2)
Term
When solving a quadratic polynomial equation, Completing The Square will work always/sometimes/never.
 Definition
always
Term
The first 2 steps of Completing The Square are always ____________ and ___________.
 Definition
Making sure the number c is on the opposite side of the equation as the other terms; dividing both sides of the equation by the number a (NOTE: it doesn't matter which of these 2 steps you do first)
Term
Determine as many ways as you can to solve the given equation:
9x^2-81=0
 Definition
Factoring (box method)
Factoring (difference of squares)
Completing the Square
Quadratic Formula
Graphing Method (graph the left side as y1 and the right as y2 and see where they intersect)
Add 81, divide by 9 and square root
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