Math 118 Quiz 3 Study Guide

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Steps for a sequence of transformation

1 / 45

46 Terms

1

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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2

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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3

Describe b=1+r

The growth factor equals the growth rate plus one

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4

Rewrite y=bˣ

x=logᵦy

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5

bʳ * bˢ = ____?

bʳ+ˢ

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6

logᵦ(rs) = ____?

logᵦr + logᵦs

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7

bʳ/bˢ = ____?

bʳ-ˢ

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8

logᵦ(r/s) = ____?

logᵦr - logᵦs

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9

(bʳ)ˢ = ____?

bʳ*ˢ

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10

logᵦ(rˢ) = ____?

s*logᵦ(r)

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11

Rewrite a=bᶜ

logᵦ(a)=c

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12

aˡᵒᵍa⁽ⁿ⁾=____?

n

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13

logₐa⁽ⁿ⁾=____?

n

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14

logₐ(x*y)=____?

logₐ(x)+logₐ(y)

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15

logₐ(x/y)=____?

logₐ(x)-logₐ(y)

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16

logₐ(xʸ)=____?

y*logₐ(x)

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17

Exponentiate m = n

a^m=a^n

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18

Take the log of m = n

logsubam = logsuban

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19

Change of base formula?

Y=b^x, x = logsubay/logsubb

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20

Amplitude formula

maximum value - minimum value / 2

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21

cos(x) = ___?

sin(x + pi/2)

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22

secant =

1/cosx

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23

cosecant =

1/sinx

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24

tangent =

sinx/cosx

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25

cotangent =

cosx/sinx

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26

What is k notation?

x = pik, where k is an integer

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27

What is the period for sin?

2pi

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28

What is the period for cos?

2pi

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29

What is the amplitude definition?

The distance from the middle to the max OR min

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30

What is the amplitude of sin?

1

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31

What is the amplitude of cos?

1

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32

Equilibrium value definition:

The middle value

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33

What is the equilibrium value of all BASE functions?

0

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34

What is the asymptote of cosecant?

vertical at intervals of pi

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35

What is the period of cosecant?

2pi

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36

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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37

What is the period of secant?

2pi

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38

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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39

What is the period of tangent?

pi

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40

What is the period of cotangent?

pi

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41

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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42

formula for sine

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

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43

What is a

amplitude

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44

what is b?

horizontal shift/compression

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45

what is c?

horizontal shift

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46

What is d?

equilibrium value

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