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Precalculus: 4.1
Precalculus: 4.1
21
Mathematics
Undergraduate 1
10/26/2015

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Term
a^x+a^y
Definition
a^(x+y)
Term
a^x/a^y
Definition
a^(x-y)
Term
(ab)^x
Definition
a^(x)b^(x)
Term
(a^x)^(y)
Definition
a^(xy)
Term
a^(0)
Definition
1
Term
a^(-x)
Definition
(1/a)^(x)
Term
Graphing an Exponential Function Where a>1
Definition
1.) Make a table of a few (the book uses seven) values of x, and corresponding values of y.
2.) Plot the points and draw a smooth curve through them
Term
Define (a^(1/n))^n
Definition
(a^(n/n))= a^1
Term
If rsubscrpt1, rsubscrpt2, rsubscrpt3, etc leads to r...
Definition
Then a^rsubscrpt1, a^rsubscrpt2, etc leads to a^r
Term
a^(1/n)
Definition
nroot a
Term
a cannot be...
Definition
1,0, or less than 0
Term
When a>1 your graph...
[Exponential Growth]
Definition
Is an increasing function
Term
When a is greater than zero and less than 1, or a^(-x), then...
[Exponential Decay]
Definition
the graph of the curve is reflected across the x-axis
Term
f(-x)
Definition
Is a reflection about the y-axis
Term
When the absolute value of a is less than one...
Definition
Then you have a horizontal stretch when..
af(x)
Term
The parent graph of an exponential function always hits the y-axis at...
Definition
Point (0,1)
Term
To find y-intercepts...
Definition
1.) Set x=0
2.) Solve
Term
Exponential functions have horizontal asymptotes but not....
Definition
Vertical or Oblique Asymptotes
Term
How do you find f(x), when given two points?
Definition
1.) Think of it as f(x)=Ca^x, in which C is your constant.
2.) If one of your points is (0,1), then that point represents your constant in the form f(0)=1.
3.) With that knowledge you can say that your other point explains the function, so let's say that the other point is (2,16). That would mean your function is f(2)=16, which means a^2=16 which means that a=4.
4.) And that is Your Answer
Term
g(x)=e^x, in which e is defined as
[Natural Exponential Function]
Definition
The horizontal asymptote of f(x)
Term
Continuous Compound Interest Formula
Definition
A=Pe^(r+t)
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