Free Printable Alg S2 Midterm Review

1.

Put these functions in order from least to greatest based on their Y-INTERCEPT. (a)

Choose from the below words

B C A

B A C

C A B

C B A

2.

Which statement below is TRUE regarding the two functions?

a)

Both functions are linear

b)

Both functions are increasing

c)

Both functions have a y-intercept of 1

d)

Both functions are exponential growth

3.

Is the equation linear, exponential, or quadratic?y = 2x+ 4 (a)

Choose from the below words

Linear

Exponential

Quadratic

None of the above

4.

Is the graph linear, exponential or neither? (a)

Choose from the below words

Linear

Exponential

Neither

5.

Is the graph linear, exponential or neither? (a)

Choose from the below words

Linear

Exponential

Neither

6.

Is the table linear, exponential or neither? (a)

Choose from the below words

Linear

Exponential

Neither

7.

Is this table linear, quadratic, exponential, or none of the above? (a)

Choose from the below words

linear

quadratic

exponential

none of the above

8.

Lee charges $3 for a basket and $2.50 for each pound of fruit picked at the orchard. Write an equation for the total cost of x pounds of fruit from the orchard. (a)

Choose from the below words

y = 3x + 2.5

y = 2.50x + 3

y = 2.50x

y = 3x + 2.50

9.

What type of function is f(x) = 2(x+4)²-7?

a)

exponential decay

b)

linear

c)

exponential growth

d)

quadratic

10.

What type of function best models the situation: A zombie virus has infected the population and the number of infected people triples every day.

a)

linear

b)

quadratic

c)

exponential growth

d)

exponential decay

11.

Which function is linear?

a)

f(x)

b)

h(x)

c)

g(x)

12.

A bank account balance earning an annual interest rate.

a)

Linear

b)

Quadratic

c)

Exponential

13.

Which function best models the amount of money you earn when you get paid an hourly wage? (a)

Choose from the below words

Linear

Quadratic

Exponential

14.

Which function best models the height and speed of throwing a ball in the air?

a)

Linear

b)

Quadratic

c)

Exponential

15.

Which situation is linear?

a)

A sample of bacteria doubles every hour

b)

The number of cars each hour on the road for a week

c)

The cost of a movie ticket increases by 5% every year

d)

The population of a town is increasing by ten people every year

16.

What type of function best models the situation: A zombie virus has infected the population and the number of infected people triples every day. (a)

Choose from the below words

Exponential growth

Linear

Quadratic

Exponential Decay

17.

Which statement below is TRUE regarding the functions pictured?

a)

Both functions have a y-intercept of 3

b)

Both functions are increasing

c)

Both functions are linear

d)

Both functions have a MULTIPLYING pattern

18.

How would you describe the rate of change of these functions?

a)

Both functions have constant rate of change because they are exponential.

b)

Both functions have a variable rate of change because they are both exponential.

c)

A has a constant rate of change because it is linear and B has a variable rate of change because it's exponential

d)

A has a constant rate of change because it is quadratic and B has a variable rate of change because it's exponential

19.

Which function is exponential?

a)

A

b)

B

c)

C

20.

What type of function describes the story below?You have $5 and triple your money every day. (a)

Choose from the below words

Linear

Quadratic

Exponential

21.

Which function would best represent each ink cartridge purchased for a printer costs $12.

a)

Linear

b)

Quadratic

c)

Exponential

22.

Give the domain and range. Tell if it is a function.

a)

D: {-4, -2, 0, 2}
R: {-2, -2, 1, 1}
Function

b)

D: {-4, -2, 0, 2}
R: {-2, 1}
Function

c)

D: {-4, -2, 0, 2}
R: {-2, -2, 1, 1}
Not a Function

d)

D: {-4, -2, 0, 2}
R: {-2, 1}
Not a Function

23.

Which model is appropriate given the points (-3, 8), (-1, 6), (0, 5), (2, 3), (3, 2)? Why?

a)

Exponential because it curves.

b)

Linear because it has a constant slope.

c)

Quadratic because it has a minimum.

d)

Infinite because it keeps going.

24.

Choose all the equations that are exponential:

a)

y = 6x -5

b)

y = 8^x - 9

c)

f(x) = 3x² + 4

d)

y = 1/3^x

e)

y = 7x³

25.

Write the function that best models the table? (a)

Choose from the below words

$y=\left(\frac{1}{4}\right)^x$

$y=\frac{1}{4}x$

$y=4x$

$y=4^x$

26.

Three functions are shown in the table. Which of the functions is exponential?

a)

f(x)

b)

g(x)

c)

h(x)

d)

None of the functions are exponential as they do not grow by equal factors over equal intervals.

27.

Three functions are shown in the table. What is the average rate of change for the function h(x) over the interval $2\le x\le4$ ?

a)

12

b)

6

c)

-6

d)

-12

28.

Lauren keeps records of the distances she travels in an Uber and what she pays.

Lauren said a linear function can represent the data that she collected (in the table). If Lauren uses the function y = mx+b what is the value of m? Explain what this value stands for in context of the problem.

a)

1.50; the amount the total cost increases for each mile driven

b)

2.25; the amount the total cost increases for each mile driven

c)

1.50; the cost with no miles driven

d)

2.25; the cost with no miles driven

29.

Which function will translate $f\left(x\right)=x^2$ left 5 units and down 1 unit?

a)

$f\left(x\right)=\left(x-1\right)^2-5$

b)

$f\left(x\right)=\left(x-5\right)^2-1$

c)

$f\left(x\right)=\left(x-5\right)^2+1$

d)

$f\left(x\right)=\left(x+5\right)^2-1$

30.

Two websites launched on the same day. At the end of the first week, the number of visitors to each website was 25. After that, the number of visitors to each website increased at different rates.

Website A: The number of visitor doubled each week

Website B: The number of visitors increased by 150 each week.

A table has been started for you. Finish it if needed to answer the question below.

Jose claims that the number of visitors to both websites can be modeled as a linear function. Is he correct?

a)

Jose is correct, both functions are linear because the number of visitors in both cases have constant differences.

b)

Jose is incorrect, only Website A has a number of visitors with equal differences.

c)

Jose is incorrect, only Website B has a number of visitors with equal differences.

d)

Jose is correct because the number of visitors in both cases have constant factors.

31.

What is the constant ratio of the table?

a)

$3$

b)

$\frac{1}{3}$

c)

$6$

d)

$1$

32.

What is the y-intercept of the graph?

a)

$21,500$

b)

$0.88$

c)

$10,000$

d)

$6$

33.

What is the domain of $y=4\left(1.2\right)^x$ ?

a)

$0<x<\infty$

b)

$All\ Real\ Numbers$

c)

$-\infty<x<4$

d)

$-4<x<\infty$

34.

What is the range of the function shown?

a)

All real numbers greater than 3

b)

All real numbers

c)

All real numbers greater than 0

d)

All real numbers greater than or equal to 0

35.

What is the asymptote of the function shown?

a)

$y=0$

b)

$y=1$

c)

$x=0$

d)

$y=-1$

36.

You buy a house for $130,000 and it appreciates 6% per year. How much is it worth in 10 years?

a)

$14,300,000

b)

$232,810

c)

$267.13

d)

$219,632

37.

Tom is losing 20% of his hair each year. If he has 1546 hairs, how much will he have in 8 years?

a)

$259$

b)

$1315$

c)

$6648$

d)

$166$

38.

A zombie outbreak is doubling daily. If there are 25 zombies, how many will there be in 7 days?

a)

$28$

b)

$175$

c)

$54,675$

d)

$3,200$

39.

What is the exponential equation for the table?

a)

$y=6\left(\frac{1}{2}\right)^x$

b)

$y=6\left(2\right)^x$

c)

$y=\frac{1}{2}\left(6\right)^x$

d)

$y=2\left(6\right)^x$

40.

What is the equation of the graph that goes through (2, -18) and (3, -54)?

a)

$y=2\left(-3\right)^x$

b)

$y=-2\left(3\right)^x$

c)

$y=3\left(-2\right)^x$

d)

$y=-3\left(2\right)^x$

41.

What is the exponential equation for the graph?

a)

$y=40\left(\frac{3}{2}\right)^x$

b)

$y=40\left(\frac{1}{2}\right)^x$

c)

$y=40\left(\frac{2}{3}\right)^x$

d)

$y=40\left(\frac{3}{4}\right)^x$

42.

What does the y-intercept represent in the word problem?

a)

The number of bounces the basketball takes

b)

The height of the basketball after the first bounce

c)

The original height of the basketball

d)

The rate at which the basketball bounces

43.

Given the table, what will be the population of mice after 8 months?

a)

$192$

b)

$3,072$

c)

$256$

d)

$1,536$

44.

Based on the graph, which statement does not appear to be true?

a)

The company opened 400 stores by the end of 1992

b)

Every year the number of stores opened increased by 25%

c)

The company opened 100 stores in 1 year

d)

Since 1992, the company has opened 250 stores each year

45.

Which best describes the graph given?

a)

Exponential Decay, asymptote at y = -1

b)

Exponential Growth, asymptote at y = 0

c)

Exponential Growth, asymptote at y = -1

d)

Exponential Decay, asymptote at y = 0

46.

Describe the transformation if f(x) = 5^x is the parent function and g(x) = 3(5)^x is the transformed function.

a)

horizontal translation right 3 units

b)

vertical translation up 3 units

c)

vertical stretch

d)

vertical compression

47.

Describe the transformation if f(x)=5^x is the parent function and g(x)=5^x+8is the transformed function.

a)

horizontal translation right 5 units

b)

vertical translation down 8 units

c)

vertical translation up 8 units

d)

vertical compression

48.

Describe the transformation if f(x) = 3(4)^x is the parent function and g(x) = 0.15(4)^x is the transformed function.

a)

vertical stretch

b)

vertical translation down 0.15 units

c)

vertical translation up 4 units

d)

vertical compression

49.

Describe the transformation if f(x) = 3(4)^x is the parent function and g(x) = -3(4)^x is the transformed function.

a)

vertical stretch

b)

reflection

c)

growth

d)

vertical compression

50.

Select all the transformations of g(x) if the parent function is f(x) = 3^x.

a)

horizontal translation left 2 units

b)

vertical compression

c)

vertical translation up 2 units

d)

vertical stretch

e)

vertical translation up .11 units

51.

Select all the transformations of g(x) if the parent function is f(x) = 3^x.

a)

vertical translation down 6 units

b)

vertical stretch

c)

vertical translation up 6 units

d)

reflection

e)

horizontal translation left 6 units

52.

Select all the transformations of g(x) if the parent function is f(x) = 3^x.

a)

vertical translation down 3 units

b)

vertical stretch

c)

vertical translation up 4 units

d)

reflection

e)

vertical compression

53.

Select all the transformations of g(x) if the parent function is f(x) = 3^x.

a)

horizontal translation right 1 unit

b)

vertical stretch

c)

vertical translation down 2 units

d)

reflection

e)

vertical compression

54.

If the blue graph is the parent function and the red the transformed function, what type of transformation occurred?

a)

vertical translation

b)

reflection

c)

vertical stretch

d)

vertical compression

55.

If the blue graph is the parent function and the red the transformed function, what type of transformation occurred?

a)

vertical translation

b)

reflection

c)

horizontal translation

d)

vertical stretch

56.

If the blue graph is the parent function and the red graph is the transformed function, what types of transformations occurred? Select all that apply.

a)

vertical translation

b)

reflection

c)

horizontal translation

d)

vertical stretch

57.

If the blue graph is the parent function and the red the transformed function, what type of transformation occurred?

a)

vertical translation

b)

reflection

c)

vertical compression

d)

vertical stretch

58.

Does the equation represent growth or decay?

$y=4\left(\frac{1}{2}\right)^x$

a)

Growth since the y-int is greater than 1.

b)

Growth since the ratio is greater than 1.

c)

Decay since the y-int is less than 1.

d)

Decay since the ratio is less than 1.

59.

What is the y-intercept of $y=\frac{3}{4}\left(4\right)^x$ ?

a)

$4$

b)

$0$

c)

$\frac{3}{4}$

d)

$3$

60.

What is the constant ratio for

$y=\frac{3}{2}\left(\frac{4}{5}\right)^x$ ?

a)

$\frac{3}{2}$

b)

$\frac{15}{8}$

c)

$12$

d)

$\frac{4}{5}$

61.

What is the rate of decay for $y=5\left(\frac{3}{4}\right)^x$ ?

a)

$5\%$

b)

$75\%$

c)

$25\%$

d)

$0.75\%$

62.

What is the constant ratio of the table?

a)

$3$

b)

$\frac{1}{3}$

c)

$6$

d)

$1$

63.

What is the y-intercept of the graph?

a)

$21,500$

b)

$0.88$

c)

$10,000$

d)

$6$

64.

What is the domain of $y=4\left(1.2\right)^x$ ?

a)

$x>0$

b)

$All\ Real\ Numbers$

c)

$x<4$

d)

$x>-4$

65.

What is the range of the function shown?

a)

All real numbers greater than 3

b)

All real numbers

c)

All real numbers greater than 0

d)

All real numbers greater than or equal to 0

66.

What is the asymptote of the function shown?

a)

$y=0$

b)

$y=1$

c)

$x=0$

d)

$x=1$

67.

You buy a house for $130,000 and it appreciates 6% per year. How much is it worth in 10 years?

a)

$14,300,000

b)

$232,810

c)

$267.13

d)

$219,632

68.

Tom is losing 20% of his hair each year. If he has 1546 hairs, how much will he have in 8 years?

a)

$259$

b)

$1315$

c)

$6648$

d)

$166$

69.

A zombie outbreak is doubling daily. If there are 25 zombies, how many will there be in 7 days?

a)

$28$

b)

$175$

c)

$54,675$

d)

$3,200$

70.

What is the exponential equation for the table?

a)

$y=6\left(\frac{1}{2}\right)^x$

b)

$y=6\left(2\right)^x$

c)

$y=\frac{1}{2}\left(6\right)^x$

d)

$y=2\left(6\right)^x$

71.

What is the exponential equation for the graph?

a)

y=40(3/2)^x

b)

y=40(1/2)^x

c)

y=40(2/3)^x

d)

y=40(3/4)^x

72.

Given the table, what will be the population of mice after 8 months?

a)

$192$

b)

$3,072$

c)

$256$

d)

$1,536$

73.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

74.

When do we have growth?
f(x) = (a)(b^x)

a)

a < 1

b)

b > 1

c)

0 < b < 1

d)

a > 1

75.

When do we have decay?
f(x) = (a)(b^x)

a)

a < 1

b)

b > 1

c)

0 < b < 1

d)

a > 1

76.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)^6

a)

Growth

b)

Decay

77.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)^3

a)

Growth

b)

Decay

78.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

79.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

a)

^.08

b)

^1.08

c)

.92

d)

8

80.

Write an exponential function to model the situation. Solve.
2) The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. What will the cost be after 4 years?

a)

C(t) = 12000(1.06)^t ; $3149.72

b)

C(t) = 12000(.06)^t ; $3149.72

c)

C(t) = 12000(.06)^t ; $1472.95

d)

C(t) = 12000(1.06)^t ; $15149.72

81.

This is the horizontal line which the values of the function cannot fall below :

a)

Asymptote

b)

Growth Factor

c)

Axis of symmetry

d)

Curve

82.

What is the constant ratio for

$y=\frac{5}{2}\left(\frac{3}{4}\right)^x$ ?

a)

$\frac{5}{2}$

b)

$\frac{15}{8}$

c)

$15$

d)

$\frac{3}{4}$

83.

Classify the model as Exponential GROWTH or DECAY.
A=1500(.90)^4

a)

Growth

b)

Decay

84.

Solve the exponential function: 5^x + 7= 32

a)

x = 25

b)

x = 6

c)

x = 9

d)

x = 2

85.

2^x - 5 = 12

a)

x = 8.5

b)

x = 4.1

c)

x = 6.2

d)

x = 3.9

86.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

87.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

a)

The predicted increase in number of elephants in the refuge each year.

b)

The predicted decrease in number of elephants in the refuge each year.

c)

The number of years it will take for the elephant population to stop increasing.

d)

The initial amount of elephants in the park.

88.

Evaluate f(-2) if f(x) = x²+ 3

a)

-1

b)

1

c)

7

d)

-7

89.

Solve the equation for x.

a)

x = 2

b)

x = 3

c)

x = 8

d)

x = 64

90.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9765

b)

9006

c)

5433

d)

9766

91.

The value of a new car depreciates (decreases) after it is purchased. Suppose that the value of the car depreciates according to an exponential decay model. Suppose that the value of the car is $12000 at the end of 5 years and that its value has been decreasing at the rate of 9% per year. Find the value of the car when it was new. Round your answer to the nearest dollar.

92.

The population of wolves, w(t) in an area is represented by the equation w(t)=800(0.95)^t where t is the number of years since the year 2000. Predict the number of wolves in the year 2012. Round to the nearest whole.

93.

Since January 1980, the population of the city of Brownville has grown according to the mathematical model, y=720,500(1.022)^xwhere x is the number of years since January 1980. If this trend continues, use this model to predict approximately when the population of Brownville will reach 1,000,000. (Round to the whole year.)

94.

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that represents the deer population. If deer population continues to grow at this rate, how many years will it take for the deer population to surpass 1000.

95.

Ngozi earns $24,000 in salary in the first year she works as an interpreter. Each year, she earns a 3.5% raise.

Write a function that gives Ngozi's salary S(t), in dollars, t years after she starts to work as an interpreter.
Do not enter commas in your answer.

S(t) =

96.

Describe the transformation if f(x)=5^x is the parent function and g(x)=3(5)^xis the transformed function.

a)

horizontal translation right 3 units

b)

vertical translation up 3 units

c)

vertical stretch

d)

vertical compression

97.

Describe the transformation if f(x)=5^x is the parent function and g(x)=5^x+8is the transformed function.

a)

horizontal translation right 5 units

b)

vertical translation down 8 units

c)

vertical translation up 8 units

d)

vertical compression

98.

Describe the transformation if f(x)=3(4)^x is the parent function and g(x)=.15(4)^xis the transformed function.

a)

vertical stretch

b)

vertical translation down .15 units

c)

vertical translation up 4 units

d)

vertical compression

99.

Describe the transformation if f(x)=3(4)^x is the parent function and g(x)=-3(4)^xis the transformed function.

a)

vertical stretch

b)

reflection

c)

growth

d)

vertical compression

100.

Select all the transformations of g(x) if the parent function is f(x)=3^x.

a)

horizontal translation left 2 units

b)

vertical compression

c)

vertical translation up 2 units

d)

vertical stretch

e)

vertical translation up .11 units

101.

Select all the transformations of g(x) if the parent function is f(x)=3^x.

a)

vertical translation down 6 units

b)

vertical stretch

c)

vertical translation up 6 units

d)

reflection

e)

horizontal translation left 6 units

102.

Select all the transformations of g(x) if the parent function is f(x)=3^x.

a)

vertical translation down 3 units

b)

vertical stretch

c)

vertical translation up 4 units

d)

reflection

e)

vertical compression

103.

Select all the transformations of g(x) if the parent function is f(x)=3^x.

a)

horizontal translation right 1 unit

b)

vertical stretch

c)

vertical translation down 2 units

d)

reflection

e)

vertical compression

104.

If the blue graph is the parent function and red the transformed function, what type of transformation occurred?

a)

vertical translation

b)

reflection

c)

vertical stretch

d)

vertical compression

105.

If the blue graph is the parent function and red the transformed function, what type of transformation occurred?

a)

vertical translation

b)

reflection

c)

horizontal translation

d)

vertical stretch

106.

If the blue graph is the parent function and red the transformed function, what types of transformations occurred? Select all that apply.

a)

vertical translation

b)

reflection

c)

horizontal translation

d)

vertical stretch

107.

If the blue graph is the parent function and red the transformed function, what type of transformation occurred?

a)

vertical translation

b)

reflection

c)

vertical compression

d)

vertical stretch

108.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

109.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

110.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

111.

What is the 14th term of the geometric sequence?

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

112.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

113.

What is the range of this graph?

a)

y = 6

b)

(0, -4)

c)

y > -6

d)

y < -6

114.

Identify the y-intercept (initial value) of the function f(x)=2(4)^x.

a)

2

b)

4

c)

(2)^x

d)

8

115.

Which of the following statement about the graph of y=6(.5)^x is TRUE?

a)

The equation of the asymptote is x=0.

b)

The y-intercept is at 6

c)

The graph is increasing

d)

The graph will never cross the y axis

116.

Look at the graph and answer each question.

Is it a growth or decay?

What is the y-intercept?

What is the asymptote?

a)

Growth

y-intercept: (0, 5)

asymptote: y = 0

b)

Decay

y-intercept: (0, 5)

asymptote: y = 0

c)

Growth

y-intercept: (0, 5)

asymptote: y = 5

d)

Decay

y-intercept: (5, 0)

asymptote: x = 0

117.

Which function models the values in the table?

a)

$f\left(x\right)=125\left(5\right)^x$

b)

$f\left(x\right)=125\left(\frac{1}{5}\right)^x$

c)

$f\left(x\right)=125-5^x$

d)

$f\left(x\right)=125-5x$

118.

What is the pattern you see in this table?

a)

Common Ratio = 1/3

b)

Common Difference = 8

c)

Common Ratio = 3

d)

Common difference = 3

119.

James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

a)

70(2)³⁵

b)

70(2)⁵

c)

2(70)⁵

d)

5(70)²

Alg S2 Midterm Review

Total questions: 119

Worksheet time: 6hrs 10mins

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