Name & Sketch

3 types of

Discontinuities

Even Function,

Odd Function

If f(-x)=f(x), then even

(symmetric about y-axis)

If f(-x)=-f(-x), then odd

(symmetric about the origin)

v is negative, backward

v is positive, forward

Area

of a

Trapezoid

(b₁+b₂)h

2

How to find

Vertical

Asymptote

How to find

inverse

switch x and y

and

solve for y

Sketch

y = x²

d: all reals

r: [0, ∞]

Pythagorean Identities

for

Trigonometry

sin²x + cos²x = 1

1 + tan²x = sec²x

1 + cot²x = csc²x

ln f

ln a

Write & sketch

the equation of

a semicircle

Point-Slope

Equation

Vertical Line

Test

Slope

Formula

Area

of

Circle

Perpendicular

Lines

Lines that have the opp.

recriprocal slopes of each other

Parallel

Lines

Equation of a

Horizontal Line

(draw horizontal line and

write its equation)

cos²u - sin²u

2 cos²u - 1

1 - 2 sin²u

Symmetric

about the

origin

A graph that looks

the same if it is rotated 180^o

about the origin

Symmetric

about the

y-axis

Mean  Value

Theorem

(aka Torres' Theorem)

If the function is continous on the closed interval [a,b] and differentiable on an open interval (a,b) then there exists a point x=c in the open interval (a,b) such that

[image]

[image]

[image][image][image]

Defintion

of

Derivative

Equation of a

Vertical Line

(draw vertical line and

write its equation)

Critical

Numbers

all possible y values a

function can output

Horizontal

Tangent

Extreme Value

Theorem

2^nd

Derivative

Test

Derivatives

DO NOT
EXIST

at...

corner

cusp

vertical tangent

discontinuity

a + v have equal sign

or

v moves away from 0

v + a have opposite signs

or

v moves towards 0

all possible x values a

function can input

Taylor

Polynomial

used to approximate functions

[image]

Newton's

Method

used to find zeroes of a function

[image]

Two Special

Trigonometric

Limits

[image]

[image]

sin x

cos x

tan x

sin x / cos x

1/cot x

Sketch

y = x³

d: all reals

r: all reals

sec x

cot x

cos x / sin x

1/tan x

csc x

Average

of

a function

if previous function, use slope formula

if function itself, use

[image]

Sketch

y = lxl

d: all reals

r: [0,∞]

How to find

Horizontal

Asymptote

If the degree of the denominator > the degree of the numerator, the horizontal asymptote is y = 0.

 
If the degree of the denominator < the degree of the numerator, there is no horizontal asymptote.

If the degrees of the numerator and denominator are equal, the horizontal asymptote = top highest exponent divided by bottom highest exponent.

for sinx, cosx, secx, and cscx,

    2π    

coef. of x

for tanx and cotx,

    π    

coef. of x

∫a^x dx

a=constant

f(x) is continuous

at x = c

means...

1. f(c) is defined

2. [image]exists

3. f(c)=[image]

Sketch

y=[image]

d: [0, ∞]

r: [0, ∞]