Math 118 Quiz 2

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Area of a circle

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60 Terms

1

Area of a circle

A=πr²

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2

Area of a rectangle

A=lw

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3

Area of a triangle

A=1/2bh

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4

Volume of a cylinder

V=πr²h

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5

Volume of a rectangular solid

V=lwh

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6

Volume of a triangular prism

V=(1/2bh)h

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7

Circumference of a circle

C=2πr

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8

Even symmetry: if _, then _

if (a,b), then (-a, b)

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9

Odd symmetry: If _, then _

if (a,b), then (-a,-b)

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10

Symmetric about the line y=x: If _, then _

If (a,b), then (b,a)

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11

What are the domain restrictions for a log function?

x > 0

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12

List the asymptotes for y=2^x

horizontal

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13

General equation for a vertical shift

f(x) + c

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14

How do you demonstrate a vertical shift on a set of points?

Either add or subtract c from the y-values

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15

General equation for a vertical stretch/compression

cf(x)

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16

When is cf(x) a vertical stretch?

when c is greater than one

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17

When is cf(x) a vertical compression?

when c is greater than zero, but less than one

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18

How do you demonstrate a vertical stretch on a set of points?

multiply y values by c

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19

How do you demonstrate a vertical compression on a set of points?

divide y values by c

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20

General equation for horizontal shift

f(x+c)

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21

How do you demonstrate a horizontal shift on a set of points?

Either add or subtract c from the x-values

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22

If c is positive during a horizontal shift, do you add or subtract c from the x-values?

subtract

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23

If c is negative during a horizontal shift, do you add or subtract c from the x-values?

add

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24

General equation for a horizontal compression/stretch

f(cx)

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25

When is f(cx) a compression?

when c is greater than one

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26

When is f(cx) a stretch?

when c is greater than one but less than zero

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27

How do you demonstrate a horizontal stretch on a set of points?

multiply x-values by the reciprocal of c

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28

How do you demonstrate a horizontal compression on a set of points?

divide x-values by c

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29

What is -f(x)?

vertical flip, reflection about the x-axis

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30

How do the points of a function change when there is a vertical flip/reflection about the x-axis?

x remains unchanged, y switches signs

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31

What is f(-x)?

horizontal flip, reflection about the y-axis

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32

How do the points of a function change when there is horizontal flip/reflection about the y-axis?

x switches signs, y remains unchanged

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33

What must you do if you have a horizontal shift and another horizontal transformation?

factor the argument to see the true shift

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34

Steps for a sequence of transformation

  1. horizontal stretch/compression

  2. horizontal shift

  3. vertical flip

  4. vertical stretch/compression

  5. horizontal flip

  6. vertical shift

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35

Recursive model equation

Ysubt = (1+n)Ysub(t-1)

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36

what is n?

the number of iterations

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37

Explicit function equation

Ysubt = (1+n)^t*ysubzero,

<p>Ysubt = (1+n)^t*ysubzero,</p>
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38

what can n be thought of as?

the independent variable

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39

what can y be thought of as?

the dependent variable

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40

when should you use recursive models?

discrete (not continuous)

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41

when should you use explicit function?

with continuous

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42

What should you do if an explicit function is used for a discrete-valued function?

restrict the domain

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43

define variable for y=ab^x

y=0 is the horizontal asymptote, a is the initial amount, b is the growth factor, and x is the number of growth periods

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44

describe b = 1 +r

the growth factor equals the growth rate plus one

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45

what is asubn?

the future value of an initial deposit

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46

compounding recursive formula?

Asubt=asub(t-1)*(1+r/n)

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47

compounding explicit formula?

A=Asubzero*e^rt

<p>A=Asubzero*e^rt</p>
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48

e=_____?

(1+I/n)^n

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49

What happens when interest is compounded more than once a year?

annual interest rate is divided by the number of compounding periods

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50
<p>(x^a)^b = _____?</p>

(x^a)^b = _____?

x^a*b

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51

Exponential graphs will contain what?

(0,1) (1,b) (-1, 1/b) and y=0

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52
<p>b^m+n=_____?</p>

b^m+n=_____?

b^m+b^n

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53

Exponential functions with a base between 0 and 1, or a negative coefficient model _____?

exponential decay

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54

(a*b)^n =______?

a^n*a^b

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55

(a^p)^q=______?

a^pq

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56

a^-p

1/a^p

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57

domain and range of y=b^x

domain: all real numbers, range y>0

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58

horizontal stretches of compression can be modeled as ____?

a change of base

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59

a horizontal shift can be modeled as?

a vertical stretch or compression

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60

What is the annual percentage yield?

effective annual rate of return taking into account the effect of compounding interest.

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