MA002-FinalExam-Answers

What is a function?

Choose one answer.

	A. A dependent quantity
	B. A rule that relates an input to exactly one output
	C. An independent quantity
	D. A combination of domain and range

Question 2

Given

and h(x)=4x+1, evaluate f(h(1)).

Choose one answer.

	A. 125
	B. 25
	C. 1
	D. 100

Question 3

Determine which toolkit function has been transformed with a horizontal shift into the graph below.

Choose one answer.

	A.
	B.
	C.
	D.

Question 4

If the graph below is reflected vertically, shifted to the left by 1, and down by 3, what is the equation of the new graph?

Choose one answer.

	A.
	B.
	C.
	D.

Question 5

Write a formula for

reflected symmetrically over the y axis, shifted up 2 units and right by 3 and horizontally stretched by 2.

Choose one answer.

	A.
	B.
	C.
	D.

Question 6

Which of the following functions does not have an inverse?

Choose one answer.

	A.
	B.
	C.
	D.

Question 7

Use the table below to find h^-1(30).

x	15	30	45	60
h(x)	20	25	30	35

Choose one answer.

	A. 15
	B. 25
	C. 45
	D. 60

Question 8

In the graph below of g(x), find g^-1(2).

Choose one answer.

	A. 1
	B. 2
	C. 3
	D. 4

Question 9

Determine the range for the piecewise function shown below in the domain [-0.5, 0.5].

Choose one answer.

	A. (1, 0)
	B. [0, 1]
	C. (-0.5, 0)
	D. (0, 0.5)

Question 10

Use a graphing calculator to graph the function

and determine the local extrema.

Choose one answer.

	A. x = -1.414, 1.414
	B. x = -1.489, 1.489
	C. x = 0
	D. x = -0.213, 0.212

Question 11

Use your graphing calculator to graph the function

and determine the intervals on which it is increasing and decreasing.

Choose one answer.

	A. Increasing on and Decreasing on
	B. Increasing on and Decreasing on
	C. Increasing on and Decreasing on
	D. Increasing on and Decreasing on

Question 12

Which of the following tables demonstrates a one-to-one function?

Table 1:

Input	Output
3	8
2	16
3	24

Table 2:

Input	Output
-2	3
0	2
2	3

Table 3:

Input	Output
-1	1
0	0
2	2

Choose one answer.

	A. Table 1
	B. Table 2
	C. Table 3
	D. None of these

Question 13

Find the equation for the graph below.

Choose one answer.

	A.
	B.
	C.
	D.

Question 14

Given the function t(s) = s³- 4s, evaluate t(4).

Choose one answer.

A. 48

B. 64

C. 112

D. -48

.

Question 15

The graph below represents which toolkit function?

Choose one answer.

A. Reciprocal

B. Square Root

C. Absolute Value

D. Quadratic

.

.

Question 16

Find the domain and range of the function, f(x) =

Choose one answer.

a. a

b. b

c. c

d. d

.

.

Question 17

Evaluate the domain and range of the function,
.

Choose one answer.

A. Domain: Range:

B. Domain: Range:

C. Domain: Range:

D. Domain: Range:

.

.

Question 18

Given the function , find the average rate of change on the interval [1, 5].

Choose one answer.

A. 10

B. 4

C. 8

D. 2

.

.

Question 19

Which of the following is true for the graph below?

Choose one answer.

A. Decreasing on the intervals

B. Concave down on

C. Concave up on

D. All of these

.

.

Question 20

Determine the inflection point(s) for the graph below.

Choose one answer.

A. x = -1 and x = 1

B. x = 0

C. x =

D. None of these

.

.

Question 21

Using the tables below, evaluate f(g(2)) and g(f(1).

x f(x)

1 3

2 6

3 9

4 12

x g(x)

1 2

2 4

3 6

4 8

Choose one answer.

A. f(g(2)) = 2, g(f(1)) = 1

B. f(g(2)) = 6, g(f(1)) = 8

C. f(g(2)) = 12, g(f(1)) = 4

D. f(g(2)) = 3, g(f(1)) = 8

.

.

Question 22

The graph below represents which toolkit function?

Choose one answer.

A. Reciprocal

B. Square Root

C. Absolute Value

D. Quadratic

.

.

Question 23

Given the function , evaluate t(9).

Choose one answer.

A. 2

B. 12.17

C. 13

D. 17

.

.

Question 24

Given the graph below, evaluate g(-1).

Choose one answer.

A. -1

B. 2

C. 1

D. 0

.

.

Question 25

Using the tables below, evaluate f(g(1)) and g(f(2)).

x f(x)

1 3

2 6

3 9

4 12

x g(x)

1 2

3 5

6 10

9 12

Choose one answer.

A. f(g(1)) = 6, g(f(2)) = 10

B. f(g(2)) = 6, g(f(1)) = 9

C. f(g(2)) = 10, g(f(1)) = 6

D. f(g(2)) = 5, g(f(1)) = 8

.

.

Question 26

The number of honey jars produced by a swarm of bees (b) is given by H = f(b). A particular forest has 3 swarms of bees that produced 12 jars of honey. Express this information in terms of the function f.

Choose one answer.

A. f(h)=b

B. f(3)=12

C. f(12)=3

D. f(1)=3

.

.

Question 27

The table below represents the dollars (in millions) of Brand X candies sold per year. Use a graphing calculator to fit a linear equation to this data.

Year 1996 1998 2000 2002 2004 2006 2008 2010 2012

$$ 1.2 1.5 1.6 1.9 2.1 2.4 2.5 2.8 3.1

Choose one answer.

A. y = 228.34x - 0.115

B. y = 0.115x - 228.34

C. y = 5x - 22.49

D. Not linear

.

.

Question 28

Given two points (2,3) and (0,6), find the slope and determine if the function is increasing or decreasing.

Choose one answer.

A. 3, decreasing

B. 2, decreasing

C. -1.5, decreasing

D. 1.5, increasing

.

.

Question 29

If f(x) is a linear function, find an equation for it given f(4) = -1 and f(9) = 2.

Choose one answer.

A.

B.

C.

D.

.

.

Question 30

Assuming a scale of 1 for the graph below, determine the slope.

Choose one answer.

A. -0.5

B. 1

C. 2.5

D. -2.5

.

.

Question 31

Jeffrey is at a coffee shop 5 miles from home. He decides to take a walk with his friend at 2 miles per hour in the opposite direction of home. Write an equation for his distance from home h hours from now.

Choose one answer.

A. d(h) = 5h + 2

B. d(h) = h - 5

C. d(h) = 2h + 5

D. d(h) = 5 - 2h

.

.

Question 32

Assuming a scale of 1, determine which graph below represents the function y = 1 + 4x.

Graph A

Graph B

Graph C

Choose one answer.

A. Graph A

B. Graph B

C. Graph C

D. None of these

.

.

Question 33

Assuming a scale of 1, determine which graph below represents the function y = 1.5 + 2.5x.

Graph A

Graph B

Graph C

Choose one answer.

A. Graph A

B. Graph B

C. Graph C

D. None of these

.

.

Question 34

Find a formula describing the change in owl population in North America if there were 280 in 2008 and 255 in 2010. (Consider 2008 to be "time 0").

Choose one answer.

A. y = 280 - 12.5x

B. y = 255 + 12.5x

C. y = 280 + 0.08x

D. y = 255 - 0.08x

.

.

Question 35

Predict the owl population in North America for the year 2014 if there were 280 in 2008 and 255 in 2010.

Choose one answer.

A. 230

B. 355

C. 330

D. 205

.

.

Question 36

You just got a new job in retail and you are given two options for your earnings:

Option 1: Base salary of $15,000 per year plus a commission of 14% of your sales.

Option 2: Base salary of $18,000 per year plus a commission of 10% of your sales.

How much money in sales would you need to make in order for Option 1 to yield a higher income than Option 2?

Choose one answer.

A. More than $12,500

B. More than $137,500

C. More than $75,000

D. More than $18,000

.

.

Question 37

A regression was run to determine if there is a relationship between how many hours of TV a person watches in a month (x) and the number of pizzas a person eats (y). Use a graphing calculator to graph this regression and predict how many pizzas a person who watches 30 hours of TV per month eats.

y = ax + b

a = -1.2

b = 38.7

Choose one answer.

A. Less than one pizza

B. Between two and three pizzas per month

C. Four pizzas

D. More than four pizzas

.

.

Question 38

Estimate the correlation coefficient for the scatter plot below.

Choose one answer.

A. -0.957

B. 0.235

C. -0.235

D. 0.869

.

.

Question 39

Given the table below which represents the dollars (in millions) of Brand X candies sold per year, determine if the trend appears linear. If so, use a graphing calculator to determine what year the dollars of candies sold will reach 3.4 million.

Year 1996 1998 2000 2002 2004 2006 2008 2010 2012

$$ 1.2 1.5 1.6 1.9 2.1 2.4 2.5 2.8 3.1

Choose one answer.

A. 2015

B. 2013

C. 2018

D. Not linear

.

.

Question 40

Given the table below, which represents the dollars (in millions) of Brand X candies sold per year, determine if the trend appears linear. If so, use a graphing calculator to determine the correlation coefficient for this regression.

Year 1996 1998 2000 2002 2004 2006 2008 2010 2012

$$ 1.2 1.5 1.6 1.9 2.1 2.4 2.5 2.8 3.1

Choose one answer.

A. 0.876

B. 0.996

C. -0.993

D. Not linear

.

.

Question 41

Solve

Choose one answer.

A.

B.

C.

D.

.

.

Question 42

Solve

Choose one answer.

A.

B.

C.

D. No solution

.

.

Question 43

Solve

Choose one answer.

A.

B.

C.

D.

.

.

Question 44

Write an equation for the following transformation of the graph below.

Move 3 units to the right

Move down 2 units

Vertical stretch such that the graph passes through the point (1,2)

Choose one answer.

A.

B.

C.

D.

.

.

Question 45

Write an expression for all values, x, within a distance of 8 from the number 3.

Choose one answer.

A.

B.

C.

D.

.

.

Question 46

Find the horizontal intercepts of the function

Choose one answer.

A. x = 5, -5

B. x = 3, -7

C. x = -3, 7

D. No horizontal intercepts

.

.

Question 47

The math grades for two students are listed below over the given time span. Which student's grade increased at a higher rate?

Year Bobby Fred

2009 75 69

2012 89 84

Choose one answer.

A. They increased at the same rate.

B. More information is needed to solve this.

C. Bobby

D. Fred

.

.

Question 48

Find the linear equation that includes these two points (2,3) and (0,6).

Choose one answer.

A. y = 2x + 3

B. y = 0.66x + 6

C. y = -6x+ 1.5

D. y = -1.5x + 6

.

.

Question 49

You go to a water park with $30. Each activity costs $3. How much money will you have left after w activities?

Choose one answer.

A. 3 - 30w

B. 30 - 3w

C. 3 = 30w

D. 3w - 30

.

.

Question 50

Graph the following functions f(x) = 3x - 2 and f(x) = 4 - x and estimate where they intersect.

Choose one answer.

A. (1.5, 2.5)

B. (0.5, 3.5)

C. (3, 7)

D. (1.7, 2.1)

.

.

Question 51

Solve

Choose one answer.

A.

B.

C.

D.

.

.

Question 52

Given the function , determine the vertical and horizontal intercepts.

Choose one answer.

A. Vertical intercept: x=2,-1, or 4; horizontal intercept: y=8

B. Vertical intercept: y=0; horizontal intercept: x=2, or -1

C. Vertical intercept: y=8; horizontal intercept: x=2,-1, or 4

D. Vertical intercept: x=2, or -1; horizontal intercept: y=8

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Question 53

Determine the number of turning points for the following graph.

Choose one answer.

A. 1

B. 2

C. 3

D. 4

.

.

Question 54

What can you conclude about the degree of the polynomal graphed below?

Choose one answer.

A. Even, degree of 2

B. Odd, degree of 3

C. Odd, degree of 5 or more

D. Even, degree of 4 or more

.

.

Question 55

What can you conclude about the long run behavior of the polynomal graphed below?

Choose one answer.

A. As and as

B. As and as

C. As and as

D. As and as

.

.

Question 56

Use the quadratic formula to solve for x in the equation

Choose one answer.

A. x = -0.477

B. x = 10.477

C. x = 0.477, -10.477

D. x = -0.477, 10.477

.

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Question 57

A ball is thrown upwards from the top of a 134 foot tall building at a speed of 129 feet per second. The ball's height above ground can be modeled by the equation . When does the ball hit the ground?

Choose one answer.

A. Impossible to calculate

B. After -1.001 seconds

C. After 27.3 seconds

D. After 1.001 seconds

.

.

Question 58

Use the quadratic formula to solve for t in the following equation:

Choose one answer.

A. t = -0.325, 12.325

B. t = 0.325, -12.325

C. t = 0, 3

D. t = -1.325, 3.325

.

.

Question 59

A ball is thrown upwards from the top of a 255 foot tall building at a speed of 249 feet per second. The ball's height above ground can be modeled by the equation . When does the ball hit the ground?

Choose one answer.

A. Impossible to calculate

B. After 0.989 seconds

C. After -0.989 seconds

D. After 28.655 seconds

.

.

Question 60

Find the equation for the graph below (assume a scale of 1 unit).

Choose one answer.

A.

B.

C.

D.

.

.

Question 61

Find the equation for the graph below (assume a scale of 1 unit).

Choose one answer.

A.

B.

C.

D.

.

.

Question 62

Use a graphing calculator to find the extrema for the function

Choose one answer.

A. Minimum: (0, -8); maximum: (-1, 0)

B. Minimum: (-2, 0); maximum: (0.67, -9.48)

C. Minimum: (0.67, -9.48); maximum: (-2, 0)

D. Minimum: (0, 0); maximum: (-1, 1)

.

.

Question 63

Find the zeros and their multiplicity for the function

Choose one answer.

A. x = -3, 3 each with multiplicity of 2

B. x = -3, -5 each with multiplicity of 1

C. x = -5, 3 each with multiplicity of 2

D. x = -3, -5, 3 each with multiplicity of 1

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Question 64

Use a graphing calculator to graph and find the extrema for the function on the interval [-3,0].

Choose one answer.

A. (-0.91, -6.47) and (-2, 0)

B. (0.42, -0.57) and (2.55, 6.94)

C. (-0.91, -6.47) and (2.55, 6.94)

D. (0.42, -0.57) and (-2, 0)

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Question 65

Sketch a graph and find the vertical asymptotes of the function

Choose one answer.

A. x = 1, -3

B. x = -1, 3

C. x = 0, -3

D. x = 2, 3

.

.

Question 66

Write an equation for the rational function graphed below.

Choose one answer.

A.

B.

C.

D.

.

.

Question 67

Write an equation for the graph below.

Choose one answer.

A.

B.

C.

D.

.

.

Question 68

Compute the inverse of the function

Choose one answer.

A.

B.

C.

D.

.

.

Question 69

Compute the inverse of the function

Choose one answer.

A.

B.

C.

D.

.

.

Question 70

Find the inverse of the function

Choose one answer.

A.

B.

C.

D.

.

.

Question 71

At a particular candy factory, a large mixing bin begins with 75 gallons of water and 4 pounds of sugar. A machine will pour in additional water at a rate of 7 gallons per minute and sugar at a rate of 1 pound per minute into the bin. Write an equation for the amount of water (w) in the bin at any given moment (t) during this process.

Choose one answer.

A. w(t)=4t+1

B. w(t)=75+7t

C. w(t)=75t+7

D. w(t)=79t+8

.

.

Question 72

At a particular candy factory, a large mixing bin begins with 75 gallons of water and 4 pounds of sugar. A machine will pour in additional water at a rate of 7 gallons per minute and sugar at a rate of 1 pound per minute into the bin. Write an equation for the concentration (c) of sugar in the bin at any given moment (t).

Choose one answer.

A.

B.

C.

D.

.

.

Question 73

Sketch a graph of the following equation and determine which graph below represents this function.

Graph A

Graph B

Graph C

Graph D

Choose one answer.

A. Graph A

B. Graph B

C. Graph C

D. Graph D

.

.

Question 74

Determine the number of local extrema for the function

Choose one answer.

A. 1

B. 2

C. 3

D. 4

.

.

Question 75

Determine the number of local extrema for the function

Choose one answer.

A. 1

B. 2

C. 3

D. 4

.

.

Question 76

Sketch a graph of the following equation and determine which graph below represents this function.

Graph A

Graph B

Graph C

Graph D

Choose one answer.

A. Graph A

B. Graph B

C. Graph C

D. Graph D

.

.

Question 77

A jewelry store has a stock of 100 necklaces. It is selling 5% of its necklaces each week (w). Write an equation demonstrating this decay.

Choose one answer.

A.

B.

C.

D.

.

.

Question 78

A jewelry store has a stock of 100 necklaces. It is selling 5% of its necklaces each week (w). Approximately how many necklaces will it have left after 12 weeks?

Choose one answer.

A. 85

B. None

C. 2

D. 54

.

.

Question 79

Find a formula for an exponential function passing through the points (-3, 8) and (3, 2).

Choose one answer.

a.

b.

c.

d.

.

.

Question 80

Determine the equation for the blue function in the graph below.

Choose one answer.

A.

B.

C.

D.

.

.

Question 81

Sketch a graph of the function and determine which function in the graph below represents it (assume a scale of 1).

Choose one answer.

A. Green

B. Red

C. Purple

D. None of these

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.

Question 82

Create an equation representing the following scenario where t stands for time in years: You invest $5,000 in an account paying 4.5% interest compounded monthly.

Choose one answer.

A.

B.

C.

D.

.

.

Question 83

If you invest $5,000 in an account paying 4.5% interest compounded monthly, how much will the account be worth in 10 years?

Choose one answer.

A. $5,190.70

B. $414,517.29

C. $5,229.70

D. $7,834.96

.

.

Question 84

Write this logarithmic equation as an exponential equation and solve for x:

Choose one answer.

A.

B.

C.

D. , x has no solution

.

.

Question 85

Use the exponent property for logs to rewrite

Choose one answer.

A.

B.

C.

D.

.

.

Question 86

Use the change of base formula to rewrite

Choose one answer.

A.

B.

C.

D.

.

.

Question 87

Solve

Choose one answer.

A. x = -8.53

B. x = -0.117

C. x = -23.82

D. x = -15.29

.

.

Question 88

A population of seagulls grows from 75 to 102 in 6 months. Find the continuous growth rate.

Choose one answer.

A. 5% per 6 months

B. .05% per month

C. .05% per 6 months

D. 5% per month

.

.

Question 89

Use the sum and difference properties of logs to write as a single logarithm.

Choose one answer.

A.

B.

C.

D.

.

.

Question 90

Expand using log properties

Choose one answer.

A.

B.

C.

D.

.

.

Question 91

Solve

Choose one answer.

A. 2

B. 54

C.

D.

.

.

Question 92

Find the domain of the function

Choose one answer.

A.

B.

C.

D.

.

.

Question 93

Find the domain of the function

Choose one answer.

A.

B.

C.

D.

.

.

Question 94

Find the range of the function

Choose one answer.

A. As and as

B. As and as

C. As and as

D. As and as

.

.

Question 95

A certain isotope decays by about 15% each day. What is the half-life of this isotope (round to the nearest day)?

Choose one answer.

A. 1 day

B. 2 days

C. 3 days

D. 4 days

.

.

Question 96

A certain isotope has a half-life of about 20 years. Find the annual decay rate.

Choose one answer.

A. 96.6%

B. 3.4%

C. 50%

D. 0.034%

.

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Question 97

A certain growth of cancerous cells increased from 400 last month to 440 this month. How long will it take for the number of cancer cells to double?

Choose one answer.

A. Less than a month

B. 6 months

C. 7.3 months

D. 1.1 months

.

.

Question 98

Find a formula for the exponential function that generated the blue line graph below. Note: the y-axis is logarithmic.

Choose one answer.

A.

B.

C.

D.

.

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Question 99

The table below represents the dollars (in millions) of Brand X candies sold per year. Use technology to fit an exponential function to this data using linearization. Then determine the percentage increase per year.

Year 1996 1998 2000 2002 2004 2006 2008

$$ 1.2 1.5 1.6 1.9 2.1 2.4 2.5

Choose one answer.

A. 6.3%

B. 2.6%

C. 52.7%

D. 5.3%

.

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Question 100

Complete the table below for the function on a semilog graph with a logarithmic scale on the vertical axis.

x log (f(x))

-2

-1

0

1

2

Choose one answer.

A. 1, 2, 4, 16, 32

B. -2, -1, 0, 1, 2

C. -0.6, -0.3, 0, 0.3, 0.6

D. 0, 0.3, 0.6, 1.2, 1.5

.

.

Question 101

Determine which function below represents

Choose one answer.

A. Red

B. Green

C. Blue

D. Cyan

.

.

	A. Domain: Range:
	B. Domain: Range:
	C. Domain: Range:
	D. Domain: Range:

	A. Decreasing on the intervals
	B. Concave down on
	C. Concave up on
	D. All of these

	A. f(g(2)) = 2, g(f(1)) = 1
	B. f(g(2)) = 6, g(f(1)) = 8
	C. f(g(2)) = 12, g(f(1)) = 4
	D. f(g(2)) = 3, g(f(1)) = 8

	A. f(g(1)) = 6, g(f(2)) = 10
	B. f(g(2)) = 6, g(f(1)) = 9
	C. f(g(2)) = 10, g(f(1)) = 6
	D. f(g(2)) = 5, g(f(1)) = 8

Year	1996	1998	2000	2002	2004	2006	2008	2010	2012
$$	1.2	1.5	1.6	1.9	2.1	2.4	2.5	2.8	3.1

	A. y = 228.34x - 0.115
	B. y = 0.115x - 228.34
	C. y = 5x - 22.49
	D. Not linear

	A. 3, decreasing
	B. 2, decreasing
	C. -1.5, decreasing
	D. 1.5, increasing

	A. d(h) = 5h + 2
	B. d(h) = h - 5
	C. d(h) = 2h + 5
	D. d(h) = 5 - 2h

	A. y = 280 - 12.5x
	B. y = 255 + 12.5x
	C. y = 280 + 0.08x
	D. y = 255 - 0.08x

	A. More than $12,500
	B. More than $137,500
	C. More than $75,000
	D. More than $18,000

	A. Less than one pizza
	B. Between two and three pizzas per month
	C. Four pizzas
	D. More than four pizzas

	A. x = 5, -5
	B. x = 3, -7
	C. x = -3, 7
	D. No horizontal intercepts

	A. They increased at the same rate.
	B. More information is needed to solve this.
	C. Bobby
	D. Fred

	A. y = 2x + 3
	B. y = 0.66x + 6
	C. y = -6x+ 1.5
	D. y = -1.5x + 6

	A. Vertical intercept: x=2,-1, or 4; horizontal intercept: y=8
	B. Vertical intercept: y=0; horizontal intercept: x=2, or -1
	C. Vertical intercept: y=8; horizontal intercept: x=2,-1, or 4
	D. Vertical intercept: x=2, or -1; horizontal intercept: y=8

	A. Even, degree of 2
	B. Odd, degree of 3
	C. Odd, degree of 5 or more
	D. Even, degree of 4 or more

	A. x = -0.477
	B. x = 10.477
	C. x = 0.477, -10.477
	D. x = -0.477, 10.477

	A. Impossible to calculate
	B. After -1.001 seconds
	C. After 27.3 seconds
	D. After 1.001 seconds

	A. t = -0.325, 12.325
	B. t = 0.325, -12.325
	C. t = 0, 3
	D. t = -1.325, 3.325

	A. Impossible to calculate
	B. After 0.989 seconds
	C. After -0.989 seconds
	D. After 28.655 seconds

	A. Minimum: (0, -8); maximum: (-1, 0)
	B. Minimum: (-2, 0); maximum: (0.67, -9.48)
	C. Minimum: (0.67, -9.48); maximum: (-2, 0)
	D. Minimum: (0, 0); maximum: (-1, 1)

	A. x = -3, 3 each with multiplicity of 2
	B. x = -3, -5 each with multiplicity of 1
	C. x = -5, 3 each with multiplicity of 2
	D. x = -3, -5, 3 each with multiplicity of 1

	A. (-0.91, -6.47) and (-2, 0)
	B. (0.42, -0.57) and (2.55, 6.94)
	C. (-0.91, -6.47) and (2.55, 6.94)
	D. (0.42, -0.57) and (-2, 0)

	A. 5% per 6 months
	B. .05% per month
	C. .05% per 6 months
	D. 5% per month

	A. 1, 2, 4, 16, 32
	B. -2, -1, 0, 1, 2
	C. -0.6, -0.3, 0, 0.3, 0.6
	D. 0, 0.3, 0.6, 1.2, 1.5