Math 118 Quiz 3 Study Guide
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1
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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
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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
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Describe b=1+r
The growth factor equals the growth rate plus one
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Rewrite y=bˣ
x=logᵦy
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bʳ \* bˢ = ____?
bʳ+ˢ
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logᵦ(rs) = ____?
logᵦr + logᵦs
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bʳ/bˢ = ____?
bʳ-ˢ
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logᵦ(r/s) = ____?
logᵦr - logᵦs
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(bʳ)ˢ = ____?
bʳ\*ˢ
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logᵦ(rˢ) = ____?
s\*logᵦ(r)
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Rewrite a=bᶜ
logᵦ(a)=c
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aˡᵒᵍa⁽ⁿ⁾=____?
n
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logₐa⁽ⁿ⁾=____?
n
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logₐ(x\*y)=____?
logₐ(x)+logₐ(y)
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logₐ(x/y)=____?
logₐ(x)-logₐ(y)
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logₐ(xʸ)=____?
y\*logₐ(x)
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Exponentiate m = n
a^m=a^n
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Take the log of m = n
logsubam = logsuban
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Change of base formula?
Y=b^x, x = logsubay/logsubb
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Amplitude formula
maximum value - minimum value / 2
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cos(x) = ___?
sin(x + pi/2)
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secant =
1/cosx
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cosecant =
1/sinx
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tangent =
sinx/cosx
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cotangent =
cosx/sinx
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What is k notation?
x = pik, where k is an integer
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What is the period for sin?
2pi
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What is the period for cos?
2pi
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What is the amplitude definition?
The distance from the middle to the max OR min
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What is the amplitude of sin?
1
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What is the amplitude of cos?
1
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Equilibrium value definition:
The middle value
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What is the equilibrium value of all BASE functions?
0
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What is the asymptote of cosecant?
vertical at intervals of pi
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What is the period of cosecant?
2pi
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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
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What is the period of secant?
2pi
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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
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What is the period of tangent?
pi
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What is the period of cotangent?
pi
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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
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formula for sine
y=Asin(B(x+c)) + D
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What is a
amplitude
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what is b?
horizontal shift/compression
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what is c?
horizontal shift
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What is d?
equilibrium value
Note 
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