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final exam

Total questions: 126

Worksheet time: 10hrs 17mins

Name
Class
Date
1.

Within which of the following segments is the function increasing and concave down?

a)

To the right of e

b)

Between b and c

c)

Between d and e

d)

Between c and d

e)

Between a and b

2.
a)
b)
c)

It is already in simplest form.

d)
e)
3.

Which of the following is equivalent to

a)
b)
c)
d)
e)
4.

What is the domain of the radical function

a)

(−∞,−1]

b)

[1,∞)

c)

(−∞,−1)

d)

(−∞,∞)

e)

[−1,∞)

5.

What values of x satisfy the equation:

a)

There are no valid solutions.

b)

𝑥=2

c)

𝑥=4

d)

𝑥= ± 4

e)

𝑥 = 16

6.

Which of the following is an inverse of the function

a)
b)
c)
d)
e)
7.

Factor the radicand of the following radical:

a)
b)
c)

This radicand can't be factored or simplified.

d)
e)
8.

Simplify the expression

a)
b)
c)

This is already as simplified as it can be

d)
e)
9.

What is the primary difference between even and odd roots? Select all of the below that are true.

a)

Odd roots need absolute values because of how the codomain of the original power functions are defined.

b)

Even roots must use restricted domains to get a partial inverse of an even power which leads to a host of nuance issues like absolute values and domain problems.

c)

Odd roots are inverses to potentially one to one functions which means it can have a domain of all real numbers and doesn't need absolute values.

d)

Even roots need absolute values because of how complex numbers work.

10.

A bacterium triples in size every 6 minutes. If you start with 3 bacterium in a dish, which of the following calculates the total amount of bacteria after t hours?

a)
b)

None of these are correct.

c)
d)
e)
11.

Which of the following is equivalent to the expression:

a)
b)

None of these are correct

c)
d)
e)
12.

Which of the following is equivalent to the expression:

a)
b)

None of these are correct

c)
d)
e)
13.

You have a student loan that accrues interest at a 12% APR (annual percentage rate). If the interest is compounded weekly, what is the growth/decay multiplier in the exponential model of how much you owe on your loan?

a)

3/1300

b)

1297/1300

c)

12

d)

1.12

e)

1303/1300

14.

Compute the following numeric exponential:

a)

343

b)

-343

c)
d)
e)

None of these are correct

15.

Which of the following intervals contains all the solutions to the equation:

a)

None of these are correct

b)

[0.5,3.1]

c)

[1.7,5.1

d)

[−1,0.75]

e)

[−3,0.2]

16.

What is the domain of function:

a)

(0,∞)

b)

[−1,∞)

c)

(−1,∞)

d)

None of these are correct

e)

(−∞,1)

17.

Which of the following is the most condensed form of the following logarithmic expression:

a)
b)
c)
d)
e)

None of these are correct

18.

Which of the following is equivalent to the logarithm

a)
b)
c)
d)
e)
19.

Which of the following is equivalent to

a)
b)
c)
d)

None of these are correct

e)
20.

What are notable features of an exponential graph? (Select all that apply)

a)

None of these are correct

b)

A horizontal asymptote

c)

A rapid vertical change after some kind of turning point.

d)

An oscillating curve (alternates between going up and down).

e)

A vertical asymptote

21.

Which of the following are key traits of a logarithmic graph? (Select all that apply)

a)

There is a horizontal asymptote

b)

The domain is closed on one side (meaning that the domain has a bracket instead of a parenthesis)

c)

There is a vertical asymptote

d)

None of these are correct

e)

The domain is open on one side (meaning that the domain has a parenthesis instead of a bracket)

22.

Consider the following graph: Which of the following could be the function that generated the above graph?

a)
b)

None of these are correct

c)
d)
e)
23.

Consider the function. What is f(9)?

a)

-18

b)

84

c)

Not enough information has been given to determine the answer.

d)

32

e)

248

24.

Consider the function. Determine if f(x) is discontinuous at 2, and if so, what type of discontinuity.

a)

Jump Discontinuity

b)

None of these are correct

c)

Asymptotic Discontinuity

d)

The function is continuous at 2.

e)

Hole Discontinuity

25.

What is the purpose of using Piece-wise functions? (Select all that apply)

a)

They give a way to treat a non-function relation as if it were a function.

b)

None of these are correct

c)

To create functions that are more difficult to understand.

d)

For use when the underlying model changes at different points of a domain

e)

To stitch together several types of functions on separate domains to make one comprehensive graph.

26.

Which of the following inequalities best models the phrase "x is at least 12 units from y''?

a)

|𝑥−12|≤𝑦

b)

|𝑥−𝑦|>12

c)

|𝑥−𝑦|≥12

d)

|𝑥−𝑦|≤12

e)

|𝑥−12|≥𝑦

27.

Find all real values of 𝑥 that satisfy the equality:|6𝑥²−4𝑥| = 10

a)

None of these are correct.

b)
c)
d)
e)

𝑥=−1

28.

Which of the following is the piecewise definition of the function 𝑓(𝑥) = | 3x + 1 |

a)
b)
c)
d)
e)
29.

What kind of things would one use absolute value for? (Select all that apply)

a)

Compound interest

b)

None of these are correct

c)

Forcing an output to be positive (eg results of even roots)

d)

Distances

e)

To stitch together several types of functions on separate domains to make one comprehensive graph.

30.

Consider the following rational function: Which of the following are domain restrictions of r(x)? (Select all that apply)

a)

𝑥≠5

b)

𝑥≠−5

c)

None of these are correct

d)

𝑥≠−3

e)

𝑥≠3

31.

Which of the following are coordinates of holes on the graph of r(x)?

a)

(-1,10)

b)

(1,-10)

c)

(1,10)

d)

(-1,-10)

e)

None of these are correct

32.

Which of the following are vertical asymptotes of ?

a)

x = 3

b)

x = 2

c)

x = -3

d)

None of these are correct

e)

x = -2

33.

Consider the following rational function:

a)

None of these are correct

b)

There is no Horizontal Asymptote

c)
d)
e)

The Horizontal Asymptote is y = 0

34.

At the Friends of the Library book sale, the books are arranged into a number of categories based on their value as follows;


Tier 1: $2.50

Tier 2: $5.00

Tier 3: $10.00


Consider the relationship that tells you all the possible books you can buy based on how much you want to pay. Is this relationship a function?

a)

Yes, each book costs one specific amount to buy.

b)

Yes, for one price you can buy many different books

c)

Yes, for one price you can buy many different books

d)

No, for one price you can buy many different books.

35.

When someone calls you and they are in your contacts, your phone uses their phone number to display their name. What are the domain and codomain of this relationship?

a)

Domain: phone numbers in your contacts; Codomain: names

b)

Domain: names; Codomain: phone numbers

c)

Domain: phone numbers; Codomain: names

d)

Domain: names in your contacts; Codomain: phone numbers

36.

Which of the following denotes a point that is left 2 and up 2 from the origin?

a)

(-2,2)

b)

None of these are correct

c)

(2,-2)

d)

(-2,2)

e)

(-2,-2)

37.

What is the primary difference between a jump discontinuity and a hole discontinuity?

a)

None of these are correct

b)

Jump discontinuities have a vertical space between the left and right segments of the graph whereas a hole is only missing a point, but the left and right sides otherwise line up.

c)

Hole discontinuities have a vertical space between the left and right segments of the graph whereas a jump discontinuity is only missing a point, but the left and right sides otherwise line up.

d)

Holes are only discontinuous at a single x value, whereas all jump discontinuities are discontinuous at more than one x value.

e)

All holes are jump discontinuities of some kind, but some jump discontinuities can have larger gaps than holes.

38.

Which of the following has an absolute maximum?

a)
b)
c)
d)
e)
39.

Which of the following is best described as a mathematical expression?

a)
b)
c)
d)

Force is mass times acceleration

e)
40.

Identify the coordinates of the points shown on the graph.

a)

a: (0,4); b: (2,1); c: (-5, -3)

b)

a: (4,0); b: (1,2); c: (-3,-5)

c)

a: (0,4); b: (-2,1); c: (5, -3)

d)

a: (-4,0); b: (-1,2); c: (-3, 5)

e)

a: (0,-4); b: (-2,-1); c: (5, 3)

41.

The function. calculates the cost of food, given a certain number of rabbits; with a missing constant 𝐶. What is the independent variable in this function?

a)

𝑟

b)

𝐶

c)

2

d)

None of these are correct

e)

𝑓

42.

What is the parent function of

a)

𝑥²

b)

None of these are correct

c)

𝑥³

d)

-3𝑥³

e)

𝑥

43.

Which of the following graphs would most properly be said to have the parent function

a)
b)
c)
d)
e)
44.

You are reviewing a model your company has to calculate the cost to modify one of your software packages for individual usage.

a)

350

b)

850

c)

$666.67

d)

$300

e)

$166.67

45.

Suppose f(x)has a zero at an x-value of 3. What would a zero of

a)

⁻³⁄₂

b)

⁻²⁄₃

c)

⅔

d)

³⁄₂

e)

6

46.

What is (𝑔∘𝑓)(𝑥)

a)
b)
c)
d)
e)
47.

What is (F−2g)(x)

a)
b)
c)
d)
e)
48.

Consider the polynomial. Which of the following statements are true?

a)

None of these are correct.

b)

Only I and IV are correct

c)

Only II and III are correct

d)

Only I is correct

e)

Only II is correct.

49.

Fully factor the following polynomial:

a)

(10𝑥−9)(𝑥+2)

b)

(𝑥−9)(𝑥+2)

c)

(2𝑥−9)(5𝑥+2)

d)

(5𝑥+9)(2𝑥−2)

e)

(5𝑥−9)(2𝑥+2)

50.

Fully factor the following polynomial:

a)
b)

9𝑥⁶-64 (It is already as factored as possible)

c)
d)
e)
51.

Consider the polynomial. What are the zeros of 3p

a)

⁻¹⁄₃ , -2, ⁻¹⁄₅

b)

⁻⁷⁄₃, -2, ⁻¹⁄₅

c)

⁻⁷⁄₃, -2, ⁹⁄₅

d)

⁻⁷⁄₃, 0, ⁻¹⁄₅

e)

⁻¹⁄₃, 0, ⁹⁄₅

52.

What is the result when dividing

a)

1

b)

0

c)
d)
e)
53.

Consider the polynomial. How many zeros does this polynomial have including complex valued zeros and counting multiplicity?

a)

12

b)

13

c)

1

d)

8

e)

It is impossible to say without factoring the polynomial

54.

Consider the function. Which of the below values are a possible number of relative extrema for this function? (Select all that apply!)

a)

13

b)

17

c)

0

d)

12

e)

18

55.

Full factor the polynomial

a)
b)
c)
d)
e)
56.

For the following graph which is the most likely parent function?

a)
b)
c)
d)
e)
57.

Fully factor the following polynomial:

a)
b)
c)
d)
e)
58.

Consider the polynomial. What are the (real-valued) zeros of 𝑝(𝑥)

a)
b)
c)
d)
e)
59.

Consider the function.Which of the below values are a possible number of absolute extrema for this function? (Select all that apply!)

a)

0

b)

1

c)

5

d)

18 / 8

e)

13

60.

Consider the polynomial. What is the sum of the zeros of 𝑝(𝑥)

a)

4

b)

1

c)
d)

-9

e)

-4

61.

Which of the following is the fully simplified form of

a)
b)
c)
d)
e)
62.

Which of the following is an inverse of the function. with the largest valid domain of𝑓(𝑥) that is inverted.

a)
b)
c)

This function cannot be inverted regardless of domain.

d)
e)
63.

Before simplifying the radical. one should convert it to which of the following?

a)
b)
c)
d)
e)
64.

Simplify the expression

a)
b)

This is already as simplified as it can be.

c)
d)
e)
65.

If 𝑎 < 𝑏 must it be true that

a)

true

b)

false

66.

You want to study the replication of a particular strain of E. coli bacteria and have the following information:
The particular strain of E. coli you want to study doubles in population after 5 hours under ideal (i.e. laboratory) conditions.

a)
b)
c)
d)
e)
67.

Which value(s) of x satisfy the equation

a)
b)

No solutions exist.

c)
d)
e)
68.

Which of the following is equivalent to the expression:

a)
b)
c)

None of these are correct

d)
e)
69.

Which of the following is equivalent to the expression:

a)

None of these are correct

b)
c)
d)
e)
70.

Your credit card company is changing their rates and sends you a promotional card to let you know the new terms.

a)
b)
c)

None of these are correct

d)
e)

$1200

71.

Compute the following numeric exponential:

a)
b)
c)
d)

None of these are correct

e)
72.

Use the properties of logarithms to simplify:

a)
b)
c)
d)
e)

None of these are correct

73.

Which of the following is equivalent to the logarithm:

a)
b)
c)

None of these are correct

d)
e)
74.

Which of the following are defining characteristics of exponential growth or decay; as oppose to other forms of increase or decrease. (Select all that apply)

a)

The difference (subtraction) between any two consecutive iteration values should be about the same.

b)

The growth/decay depends on the amount there currently is.

c)

The growth/decay rate is constant; ie the same amount is added or subtracted each iteration

d)

The ratio between any two consecutive iterations should be approximately the same value.

e)

The growth/decay rate is very fast.

75.

UNFIN Which of the following are key traits of a logarithmic graph? (Select all that apply)

a)

The domain is open on one side (meaning that the domain has a parenthesis instead of a bracket)

b)

The domain is closed on one side (meaning that the domain has a bracket instead of a parenthesis)

c)

There is a horizontal asymptote

d)

There is a vertical asymptote

e)

None of these are correct

76.

Consider the function. What is f(2)?

a)
b)

-10

c)

-12

d)

-2

e)

None of these are correct

77.

Consider the following rational function: Which of the following are coordinates of holes on the graph of r(x)? (Select all that apply)

a)
b)
c)

(5,0)

d)

(2,0)

e)

None of these are correct

78.

Consider the following rational function:

a)

There is no Horizontal Asymptote

b)

The Horizontal Asymptote is y=1

c)

The Horizontal Asymptote is y=18

d)

None of these are correct

e)

The Horizontal Asymptote is y=0

79.

A university parking lot designates spaces based on parking permit colors. The lot has 6 rows of 12 parking spaces each.

a)

YES

b)

NO

80.

A function that determines what a house costs (in dollars), dependent on it's square footage has a domain of:

a)

square footage of houses/money (in dollars)

b)

square footage of houses/ size of houses

81.

Which of the following graphs depicts a continuous relationship?

a)
b)
c)
d)
e)
82.

What is the remainder when. is divided by

a)

244

b)

208

c)

-244

d)

0 (There is no remainder)

e)
83.

Full factor the polynomial

a)
b)
c)
d)
e)
84.

Which of the following is the graph of

a)
b)
c)
d)
e)
85.

Which of the following is equivalent to the expression

a)
b)
c)
d)
e)
86.

What is the domain of the real-valued (ie no non-real numbers allowed) function

a)

(−∞,1]

b)

(−∞,∞)

c)

[−1,∞)

d)

(−∞,1)

e)

(−∞,3]

87.

What value(s) of x satisfy the equation:

a)
b)
c)
d)
e)

There are no valid solutions.

88.

Simplify the expression

a)
b)
c)
d)
e)

This is already as simplified as it can be

89.

Which of the following intervals has the solution to the equation:

a)

[−9,−4.3]

b)

[−1.2,0.5]

c)

None of these intervals contain the correct answer.

d)

[3.4,8.1]

e)

[0,2.2]

90.

Which of the following is equivalent to the expression

a)
b)
c)
d)
e)
91.

What is the domain of function:

a)

(2,∞)

b)

None of these are correct

c)

(−∞,−2)

d)

(−2,∞)

e)

(−∞,2)

92.

Which of the following is equivalent to the logarithm

a)
b)
c)
d)
e)
93.

Which of the following is equivalent to log

a)
b)
c)
d)

None of these are correct

e)
94.

Consider the following graph: Which of the following could be the function that generated the above graph? (Hint: Compare points on the graph to points of the function)

a)
b)
c)
d)
e)

None of these are correct

95.

Consider the function. What is f(4)?

a)

630

b)

3

c)

-21

d)

None of these are correct

e)

-13

96.

Consider the following rational function: Which of the following are domain restrictions of r(x)? (Select all that apply)

a)

𝑥 ≠ 5

b)

None of these are correct

c)

𝑥 ≠ 4

d)

𝑥 ≠ −4

e)

𝑥 ≠ −5

97.

Consider the following rational function: Which of the following are vertical asymptotes of ? (Select all that apply)

a)

None of these are correct

b)

x = -5

c)

x = 5

d)

x = -2

e)

x = 2

98.

Which coordinates describe a point that is 5 units up and 2 units to the left of the origin?

a)

(2, -5)

b)

(-5, 2)

c)

(5, -2)

d)

(5, 2)

e)

(-2,5)

99.

What is the fully factored form (with real coefficients) for the polynomial

a)
b)
c)
d)
e)
100.

Consider the polynomial. How many zeros does this polynomial have including complex valued zeros and counting multiplicity?

a)

1

b)

12

c)

It is impossible to say without factoring this polynomial.

d)

9

e)

19

101.

Fully factor the polynomial:

a)
b)
c)
d)
e)
102.

Simplify the numeric radical

a)
b)
c)
d)
e)
103.

Which real value(s) of x satisfy the equation

a)

No real solutions.

b)
c)
d)
e)
104.

A particular isotope has a half life of 7 years (that is; the amount of material remaining is cut in half every seven years). How long would it take before three quarters of the starting material has decayed?

a)

7 years

b)

14 years

c)

About 3 years

d)

21 years

e)

There is not enough information to answer this question.

105.

Which of the following is equivalent to the expression

a)
b)
c)
d)

None of these are correct

e)
106.

You take out a personal loan for $4000 with an interest rate of 4% a month, compounded four times a month. What is the model to determine how much you owe if you don't make any payments, after 𝑡

t months?

a)
b)
c)

None of these are correct

d)
e)
107.

Which of the following intervals contains all the solutions to the equation:

a)

None of these are correct

b)

[0.5,3.5]

c)

[−0.5,1.5]

d)

[3.7,5.1]

e)

[−5.2,−3.3]

108.

Which of the following is the most condensed form of the following logarithmic expression:

a)
b)
c)
d)

None of these are correct

e)
109.

Which of the following is equivalent to the logarithm:

a)
b)
c)

None of these are correct

d)
e)
110.

Which of the following would be best modeled by logarithms? (Select all that apply)

a)

Money in a retirement account over time.

b)

Amount of radioactive substance left after a certain amount of time.

c)

Compound interest

d)

Bacterial Growth

e)

None of these are correct

111.

Consider the following rational function: Which of the following are domain restrictions of r(x)? (Select all that apply)

a)

None of these are correct

b)

𝑥≠ 5

c)

𝑥≠ −2

d)

𝑥≠ 2

e)

𝑥≠ −5

112.

Consider the following rational function: Which of the following are coordinates of holes on the graph of r(x)? (Select all that apply)

a)

(5,0)

b)

None of these are correct

c)

(−5,8)

d)

(−5,0)

e)
113.

Which of the following equations are polynomials?

a)

All of them are Polynomials.

b)

IV Only.

c)

I and II Only.

d)

I, II, and III Only.

e)

I Only.

114.

Consider the polynomial. Which of the following are true?

a)

Only I, III, and IV are correct.

b)

Only I, II and IV are correct

c)

Only I and IV are correct

d)

Only I is correct

e)

All of these are correct.

115.

What can be said about the extrema of 𝑝(𝑥).

a)

There is nothing we can deduce about the extrema of 𝑝(𝑥)

without a graph.

b)

p(x) does have an absolute extrema and it has at most 9 local extrema.

c)

p(x) does not have an absolute extrema and it has at most 8 local extrema.

d)

p(x) does not have an absolute extrema and it has at most 9 local extrema.

e)

p(x) does have an absolute extrema and it has at most 8 local extrema.

116.

Simplify the numeric radical

a)
b)
c)
d)
e)
117.

Compute the following numeric exponential:

a)

-32

b)

32

c)

None of these are correct

d)
e)
118.

Which value of x satisfies the equation

a)
b)
c)

No real solutions.

d)

x = -½

e)

x = ³⁄₂

119.

Which of the following is equivalent to

a)

None of these are correct

b)
c)
d)
e)
120.

Which of the following would be likely situations to use exponential growth or decay type models? (Select all that apply)

a)

Compound interest

b)

Amount of radioactive material remaining over time.

c)

Bacterial growth

d)

Amount in a non-interest earning bank account with a regular salary being deposited every week.

e)

None of these are correct

121.

Consider the function. Determine if f(x) is discontinuous at 4, and if so, what type of discontinuity.

a)

Asymptotic Discontinuity

b)

The function is continuous at 4.

c)

Hole Discontinuity

d)

None of these are correct

e)

Jump Discontinuity

122.

At the Friends of the Library book sale, the books are arranged into a number of categories based on their value as follows;

a)

C = xyz

b)

C = (2.5x)(5y)(10z)

c)

C = 17.5(x+y+z)

d)

C = 2.5x+5y+10z

e)

C = x+y+z

123.

Fully factor the following polynomial:

a)
b)
c)

25(𝑥−1)² (𝑥+1)²

d)

25(𝑥+1)⁴

e)

25(𝑥²−1)²

124.

Consider the polynomial. Which of the following can not be a root of the polynomial? (Hint: Use Rational Root Theorem)

a)

2𝑥−19

b)

7𝑥−323

c)

17𝑥−7

d)

7𝑥−19

e)

2𝑥−17

125.

What is the domain of the real-valued function

a)

(−∞, ¹⁷⁄₃ ]

b)

All real numbers.

c)

[ ¹⁷⁄₃, ∞)

d)

[ - ¹⁷⁄₃ , ∞)

e)
126.

What does it mean to increase logarithmically?

a)

The growth rate is very fast.

b)

The more of something you have, the slower it increases.

c)

The growth rate is very slow.

d)

The more of something you have, the faster it grows.

e)

None of these are correct

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