Math 118 Quiz 3 Study Guide

Steps for a sequence of transformation

1. Horizontal shift/compression
2. Horiztonal stretch
3. Vertical reflection
4. Vertical shift/compression
5. Horizontal reflection
6. Vertical shift

Define the variables for y=a(bˣ)+c

A is the initial amount (amount at zero), b is the growth factor, x is the number of growth periods and c is the horizontal asymptote

Describe b=1+r

The growth factor equals the growth rate plus one

Rewrite y=bˣ

x=logᵦy

bʳ * bˢ = ____?

bʳ+ˢ

logᵦ(rs) = ____?

logᵦr + logᵦs

bʳ/bˢ = ____?

bʳ-ˢ

logᵦ(r/s) = ____?

logᵦr - logᵦs

(bʳ)ˢ = ____?

bʳ*ˢ

logᵦ(rˢ) = ____?

s*logᵦ(r)

Rewrite a=bᶜ

logᵦ(a)=c

aˡᵒᵍa⁽ⁿ⁾=____?

n

logₐa⁽ⁿ⁾=____?

n

logₐ(x*y)=____?

logₐ(x)+logₐ(y)

logₐ(x/y)=____?

logₐ(x)-logₐ(y)

logₐ(xʸ)=____?

y*logₐ(x)

Exponentiate m = n

a^m=a^n

Take the log of m = n

logsubam = logsuban

Change of base formula?

Y=b^x, x = logsubay/logsubb

Amplitude formula

maximum value - minimum value / 2

cos(x) = ___?

sin(x + pi/2)

secant =

1/cosx

cosecant =

1/sinx

tangent =

sinx/cosx

cotangent =

cosx/sinx

What is k notation?

x = pik, where k is an integer

What is the period for sin?

2pi

What is the period for cos?

2pi

What is the amplitude definition?

The distance from the middle to the max OR min

What is the amplitude of sin?

1

What is the amplitude of cos?

1

Equilibrium value definition:

The middle value

What is the equilibrium value of all BASE functions?

0

What is the asymptote of cosecant?

vertical at intervals of pi

What is the period of cosecant?

2pi

What is the domain and range of cosecant?

domain is x such x does not equal pik, and is an integer. Range is y such that y is greater than or equal to one OR less than or equal to negative one

What is the period of secant?

2pi

What is the domain and range of secant?

domain is x such that x is not equal to pi/2 + k, and k is an integer. range is y such that y is greater than or equal to one OR less than or equal to negative one

What is the period of tangent?

pi

What is the period of cotangent?

pi

What is the domain and range of tangent?

domain is x such that x does not equal pi/2 +pik, and the range is all real numbers

formula for sine

y=Asin(B(x+c)) + D

What is a

amplitude

what is b?

horizontal shift/compression

what is c?

horizontal shift

What is d?

equilibrium value