Precalculus

Midpoint Formula

Distance Formula

Equation of a Circle

Slope Equation

Point-Slope Formula

Domain

refers to x-values

Range

refers to y-values

Zeros of a function f(x) is...

x-values for which f(x)=0

y-axis Symmetry

even functions

Origin Symmetry

odd functions

Even Functions

f(-x) = f(x)

Odd Functions

f(-x) = -f(x)

f(x)=x^2

f(x)=x^3

f(x)=|x|

f(x)=1/x

f(x)=1/x^2

f(x)=(root)x

f(x)=(cube root)x

Shift up by c

f(x)+c

Shift down by c

f(x)-c

Shift left by c

f(x+c)

Shift right by c

f(x-c)

Reflect About x-axis

-f(x)

Reflect About y-axis

f(-x)

Vertical Stretch

c(f(x))

Vertical Shrink

f(x)/c

Horizontal Stretch

f(x/c)

Horizontal Shirnk

f(cx)

What function has no inverse?

f(x)^2

f(x) has an inverse if it passes what test

horizontal line test

Steps for Finding Inverse Functions

1) write f(x) as y

2) interchange x and y

3) solve for y in terms of x

4) write y as f^-1(x)

General Quadratic Form

f(x)=ax^2+bx+c

Vertex Form

f(x)=a(x-h)^2+k

(h, k) = vertex

x=h = axis of symmetry

(positive)x^(even)

rises to the left, rises to the right

(negative)x^(even)

falls to the left, falls to the right

(positive)x^(odd)

falls to the left, rises to the right

(negative)x^(odd)

rises to the left, falls to the right

Standard From for Complex Numbers

a+bi

i^1

i

i^2

-1

i^3

-i

i^4

1

Exponential Function

3^x

Power Function

x^3

Annual Compound Formula

y=P(1+r)^t

Continuous Compound Formula

y=Pe^rt

Compound n Times per Year Formula

y=P(1+r/n)^nt

Circumference

The distance around a circle, C=2πr

Arc Length

secant(in rad) x r

Area of a Circle Segment

(1/2) x secant(in rad) x r^2

Convert Degrees to Radian

multiply by 180(degrees)/pi

Convert Radians to Degrees

multiply by pi/180(degrees)

sin x

opp/hyp

cos x

adj/hyp

tan x

opp/adj

unit circle

Reciprocal Identities

csc(x)=1/sin(x)

sec(x)=1/cos(x)

cot(x)=1/tan(x)

Quotient Identities

tan(x)=sin(x)/cos(x)

cot(x)=cos(x)/sin(x)

Pythagorean Identities

sin^2(x) + cos^2(x) = 1

1 + tan^2(x) = csc^2(x)

1 + cot^2(x) =csc^2(x)