Math 118 Exam 1 Study Guide

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Area of a circle

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76 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

Pythagorean theorem

a^2+b^2=c^2

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9

Even symmetry: if _, then _

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

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10

Odd symmetry: If _, then _

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

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11

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

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

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12

Describe the symmetry between f(x) and the inverse of f(x)

symmetric about the line y=x

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13

When evaluating a problem and you do not find an answer then it is

undefined

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14

When solving a problem and you do not find an answer then it is

no solution

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15

Is it okay for multiple inputs to give the same output?

yes

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16

Is it okay for one input to give multiple outputs?

no

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17

What are the domain restrictions for a log function?

x > 0

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18

What is the criteria for functions to be identical/equivalent?

they must have the same domain and ALL the same points

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19

List the asymptotes for y=2^x

horizontal

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20

List the asymptotes for y=1/x

horizontal and vertical

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21

List the asymptotes for a log function

vertical

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22

What is a correspondence that maps EACH element in x to a UNIQUE element in y?

function

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23

Name the other terms for input (there's 4)

x, domain, independent variable, argument

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24

Name the other terms for output (there's four)

y, range, dependent variable, value

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25

What is evaluating?

finding an output for the given input (at most one answer)

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26

What is solving?

finding all inputs for a given output (infinite answers)

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27

What is finding?

either evaluating, solving, or finding an expression

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28

What is an increasing function?

<p></p>
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29

What is a decreasing function?

<p></p>
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30

What is a concave up function?

<p></p>
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31

What is a concave down function?

<p></p>
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32

If a function has even symmetry then f(-x) =

f(x)

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33

If a function has odd symmetry then f(-x) =

-f(x)

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34

What are three domain restrictions?

can't divide by zero, can't take the square root of a negative number, can't take the log of a negative number or zero

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35

When do you need a sign chart?

if multiple linear factors are in the same even root or the same log

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36

What is an equation for the thing you want to maximize or minimize called?

objective function

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37

If the objective function has more than one input variable, you must find any equations that relate to your input variables. What are these called?

constraint equations

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38

General equation for a vertical shift

f(x) + c

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39

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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40

General equation for a vertical stretch/compression

cf(x)

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41

When is cf(x) a vertical stretch?

when c is greater than one

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42

When is cf(x) a vertical compression?

when c is greater than zero, but less than one

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43

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

multiply y values by c

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44

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

divide y values by c

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45

General equation for horizontal shift

f(x+c)

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46

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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47

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

subtract

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48

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

add

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49

General equation for a horizontal compression/stretch

f(cx)

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50

When is f(cx) a compression?

when c is greater than one

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51

When is f(cx) a stretch?

when c is greater than one but less than zero

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52

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

multiply x-values by the reciprocal of c

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53

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

divide x-values by c

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54

What is -f(x)?

vertical flip, reflection about the x-axis

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55

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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56

What is f(-x)?

horizontal flip, reflection about the y-axis

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57

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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58

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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59

Steps for a sequence of transformation

horizontal shift -> stretches/compressions -> reflections -> vertical shifts

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60

When should you plug points into the equation to check you did the transformation correctly?

always

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61

___________ is the set of numbers in the domain in the domain of a resulting composite function AND the domain of the inner function.

domain of a composite function

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62

In order to ensure a composite function remains a function, you need _____

domain restrictions

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63

How do you find inverses algebraically?

switch x and y and solve for y

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64

The input of f is the _____ of f inverse.

output

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65

The input of f inverse is the _____ of f.

output

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66

If the point (a,b) is on f, then the point _____ is on f inverse.

(b,a)

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67

Are the domain and range of f and f inverse the same?

no, they switch

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68

f^1(x) is the _____. (f(x))^1 is the ______.

inverse, reciprocal

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69

What do you do if a function is not one-to-one?

restrict it's domain

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70

Draw y = |x|

knowt flashcard image
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71

Draw y=x^2

knowt flashcard image
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72

Draw y=x^3

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73

Draw y=√x

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74

Draw y=2^x

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75

Draw y=1/x

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76

Draw y=sin(x)

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