Name:_______________________ Date:__________________

Unit 3 Multiple Choice Test Questions

MCC9‐12.F.IF.1_____ Understand that a function from one set (called the domain) to another set (called the range) as-signs to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). (Draw examples from linear and exponential functions.) Directions: Determine if the following representations are functions. State Function or Not a Function

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

Multiple Choice Identify the choice that best completes the statement or answers the question.

1. Give the domain and range of the relation. (F.IF.5) x y 4 9 6 13 0 0

–5 –9

a. D: {–5, 0, 4, 6}; R: {–9, 0, 9, 13} b. D: {–5, 4, 6}; R: {–9, 9, 13} c. D: {4, 6, –5, 9, 13, –9}; R: {0} d. D: {–9, 0, 9, 13}; R: {–5, 0, 4, 6}

2. Determine a relationship between the x- and

y-values. Write an equation. (BF.1) x 1 2 3 4 y –4 –3 –2 –1

a. y = x – 5 b. y = –5x + 1 c. y = x – 2 d. y = –x – 5

3. For , find f(1).(F.IF.1, 2) a. 10 b. 2 c. –13 d. –8

4. (F.IF.4)Find the x- and y-intercepts. a. x-intercept: –4, y-intercept: –2

b. x-intercept: –4, y-intercept: 2 c. x-intercept: 4, y-intercept: 2 d. x-intercept: 2, y-intercept: –4

5. Let be the transformation, vertical translation

3 units down, of . Write the rule for . (BF.3)

a. b. c. d.

6. Give the domain and range of the relation.

7. Clayton has 65 stamps in her collection. To expand the collection, he is planning to buy some books of stamps that

have 16 stamps each. All of the books cost the same. Clayton is not sure yet about the number of books of stamps he wants to buy, but he has enough money to buy up to 5 of them. Write a function to describe how many stamps Clayton can buy. Let x represents the number of books of stamps Clayton buys. Find a reasonable domain and range for the function. a. ; D: {0, 1, 2, 3, 4}; R: {65, 81, 97,

113, 129} b. ; D: {5}; R: {145} c. ; D: {1, 2, 3, 4}; R: {81, 97, 113,

129, 145} d. ; D: {0, 1, 2, 3, 4, 5}; R: {65, 81,

97, 113, 129, 145}

8. Find the 23rd term in the arithmetic sequence 3, 11, 19, 27, 35,... a. 179 b. 157 c. 176 d. 187

9. Sylvie is going on vacation. She has already driven 46 miles in one hour. Her average speed for the rest of the trip is

64 miles per hour. How far will Sylvie have driven 6 hours later? a. 276 miles b. 366 miles c. 384 miles d. 430 miles

10. Tell whether the set of ordered pairs satisfies a linear function. Explain.

a. No; there is a constant change in x that corresponds to a constant change in y.

b. No; there is no constant change in x that corresponds to a constant change in y.

c. Yes; there is a constant change in x that corresponds to a constant change in y.

d. Yes; there is no constant change in x that corresponds to a constant change in y.

a. D: {–2, 4, 5, 9}; R: {0, 3, 8} b. D: {0, 3, 8}; R: {–2, 4, 5, 9} c. D: ; R: d. D: ; R:

11. Find the slope of the line described by 3x + 4y = 12.

a. b. c. d.

12. Find the x- and y-intercepts of .

a. x-intercept: 5, y-intercept: b. x-intercept: , y-intercept: –10 c. x-intercept: 5, y-intercept: –10 d. x-intercept: , y-intercept:

13. Find the slope of the line.

a. b. c. d.

− 34

− 43

34

43

−96

6 −9

23

− 32

− 23

13

14. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line. Then tell what rate the slope represents.

a. The slope is . The slope means that the

amount of money in the account is decreasing at a rate of $50 every week.

b. The slope is 50. The slope means that the amount of money in the account is increasing at a rate of $50 every week.

c. The slope is . The slope means that the amount of money in the account is decreasing at a rate of $0.02 every week.

d. The slope is . The slope means that the amount of money in the account is decreasing at a rate of $50 every 2 weeks.

16. The water level of a river is 34 feet and it is receding at a rate of 0.5 foot per day. Write an equation that represents the

water level, w, after d days. Identify the slope and y-intercept and describe their meanings. In how many days will the water level be 26 feet? a.

The slope is 34, and this is the rate at which the water level is receding. The y-intercept is 0.5, and this is the water level after 0 days. In 16 days, the water level will be 26 feet.

b. The slope is , and this is the rate at which the water level is receding. The y-intercept is , and this is the water level after 0 days. In 120 days, the water level will be 26 feet.

c. The slope is 34, and this is the rate at which the water level is receding. The y-intercept is , and this is the water level after 0 days. In 120 days, the water level will be 26 feet.

d. The slope is , and this is the rate at which the

Time (weeks)

Am

ount

($)

(12, 2000)(4, 2400)

2 4 6 8 10 12 14 16 18 20 22

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

water level is receding. The y-intercept is 34, and this is the water level after 0 days. In 16 days, the water level will be 26 feet.

17. Let be the transformation, vertical translation 4 units down, of . Write the rule for . a. b. c. d.

Use the following context to answer questions 18-19. (F.BF.1, F.BF.1a, F.IF.3)

Carlos begins with 8 baseball cards in his collection one month. Each month, he increases his collection by 2 baseball cards. The table below shows the month number and the number of cards in Carlos’ collection.

Month Number Number of Baseball Cards

1 8

2 10

3 12

4 14

5 16

6 18

18. Express the function of Carlos’ baseball cards as a sequence in explicit form. a. 𝑎𝑛 = 2𝑛 + 6 b. 𝑎𝑛 = 𝑛 + 2 c. 𝑎𝑛 = 𝑛 + 8 d. 𝑎𝑛 = 2𝑛 + 8

19. Express the function of Carlos’ baseball cards as a sequence in recursive form. a. 𝑎𝑛 = 𝑎𝑛−1 + 6 b. 𝑎𝑛 = 2𝑎𝑛−1 + 6 c. 𝑎𝑛 = 𝑎𝑛−1 + 2 d. 𝑎𝑛 = 2𝑎𝑛−1

(CCGPS: F.BF.2)

20. Given the recursive form of the following function, determine the first 4 terms in the sequence. 1

1

13n n

aa a −

==

a. 1, 3, 6, 9 b. 1, 3, 9, 27 c. 1, 2, 3, 4 d. 1, 4, 7, 10

21. Given the explicit form of the following function, determine the first 4 terms in the sequence. 𝑎𝑛 = −𝑛 + 3

a. 3, 2, 1, 0 b. -1, 2, 5, 8 c. 2, 1, 0, -1

d. 1, 2, 3, 4

Use the following context to answer questions 22-24. (CCGPS: F.BF.1, F.BF.1a, F.1f. 7e, F.LE.1, F.LE.2)

John took a sample of water from the pond behind his house. On the first day, he found 1 bacteria in the sample. Each day that amount tripled. The table for one week of bacteria growth is in the sample is shown below.

Day Number of Bacteria

1 1

2 3

3 9

4 27

5 81

6 243

7 729

22. Can this problem situation be described as a linear function or exponential function? How do you know?

a. Linear, because the common ratio is 3. b. Linear, because the common difference is 3. c. Exponential, because the common ratio is 3.

d. Exponential, because the common difference is 3.

23. Write an explicit rule for the problem situation from above. a. 𝑎𝑛 = 3𝑛−1 b. 𝑎𝑛 = 3𝑛 c. 𝑎𝑛 = 1𝑛−1 d. 𝑎𝑛 = 3𝑛−1 + 1

24. Write a recursive rule for the problem situation above.

a. 𝑎𝑛 = 9𝑎𝑛−1 b. 𝑎𝑛 = 3𝑎𝑛−1 c. 𝑎𝑛 = 𝑎𝑛−1 + 3 d. 𝑎𝑛 = 𝑎𝑛−1 − 3

The following two functions are graphed below. Use them to answer questions 25-27. (CCGPS: F.LE.3)

( ) 4 4( ) 2 3x

f x xg x

= +

= +

25. What type of function is f(x) and how do you know?

f(x)

g(x)

a. Exponential, because there is an x in the equation. b. Linear, because the rate of change is constant c. Exponential, because the variable is exponent. d. Linear, because there is an x in the equation.

26. Which one of the following characteristics is true for both f(x) and g(x).

e. They both have a constant rate of change. f. They both have a y-intercept of (0, 4). g. They both are decreasing over all x-values. h. The both have a range of all real numbers.

27. What is the range of g(x)?

i. [3, ∞) j. (3, ∞) k. All real numbers l. (0, ∞)

Given the functions ( ) 5 2f x x= − and ( ) 4xg x = , answer questions 28-30. (CCGPS:F.BF.1b)

28. Find (3) (2)f g+ . a. 29 b. 3 c. 72 d. 56

29. Find 3 (1) 4 (2)g f− . e. 0 f. 44 g. 20 h. -20

30. Find f(x) + g(x).

i. x – 2 j. 5𝑥 + 4𝑥 − 2 k. 5𝑥 + 4𝑥 l. 5𝑥 − 2 − 4𝑥

(CCGPS: F.BF.3)

31. Sarah graphed the equation, 𝑓(𝑥) = 3𝑥 on the coordinate plane below. Her partner graphed g(x) on the same coordinate plane below. Find the function equation for g(x).

m. 𝑔(𝑥) = 3𝑥 + 4 n. 𝑔(𝑥) = 3𝑥 − 4 o. 𝑔(𝑥) = 4 ∙ 3𝑥 p. 𝑔(𝑥) = 3𝑥

32. Given the function 𝑓(𝑥) = 2𝑥 , find a function for g(x). q. 𝑔(𝑥) = 2𝑥 r. 𝑔(𝑥) = 2𝑥 + 4 s. 𝑔(𝑥) = 2𝑥 − 4 t. 𝑔(𝑥) = 4 ∙ 2𝑥

33. If the original function is 𝑓(𝑥) = 2𝑥, and you shifted it to the right 5. What would be the correct equation for the new, transformed function? u. 𝑓(𝑥) = 2𝑥 − 5 v. 𝑓(𝑥) = −5 ∙ 2𝑥 w. 𝑓(𝑥) = 2𝑥−5 x. 𝑓(𝑥) = 2𝑥+5

Forevermore is a band made up of 3 of your friends. They have recorded a CD and would like to burn CDs to sell. They found two recording companies that will make a master CD and design the cover art, then make

copies of the CDs. Company A charges $100 to make the master CD and design the cover art and an addi-tional $3 per CD to make copies. Company B charges $5 per CD with no initial charge for the master CD and cover art. (A.REI.10, A.REI.11. F.IF.2, F.IF.7, F.IF.9, F.BF.1)

34. Which equation represents the total cost, 𝐶, of using company A if x represents the total number of CDs produced.

a) 𝐶 = 100𝑥 + 3 b) 𝐶 = 3𝑥 + 100 c) 𝐶 = 5𝑥 + 100 d) 𝐶 = 105𝑥

35. Give the total cost Forevermore must pay if they record 75 CDs using each company. a) Company A: $7,503; Company B: $7,875 b) Company A: $225; Company B: $75 c) Company A: $325; Company B: $375 d) Company A: $400; Company B: $500

36. Which below shows the correct table of values for Company A? a.

Number of burned CDs

0 25 50 75 100

Total Cost

100 175 250 325 400

b.

c.

37. Which of the following is false about the graphs the number of CDs and total cost for each company?

a) Both graphs have a positive rate of change (slope)

Number of burned CDs

0 25 50 75 100

Total Cost

0 125 250 375 500

Number of burned CDs

0 25 50 75 100

Total Cost

125 200 275 350 425

b) Company A has a y-intercept at (0, 100) and Company B has a y-intercept at (0, 0). c) Their intersection point is where the amount of CDs ordered costs the same for each company. d) The graphs do not intersect.

38. If you are ordering more than 50 CDs, which company would be the cheapest? a) Company A b) Company B

39. Which mapping below represents a function? a) Mapping A b) Mapping B

A B

Given functions ( ) 3 1f x x= − and ( ) 2xg x = . (F.IF.1, F.IF.2)

Find: Answer Choices:

40. ( 2)f − a) 8

41. (3)g b) -7 c) 3m-1

42. ( )f m

43. Which of the following models an exponential function? (F.LE.1)

a) Stew gets paid $12 per hour to cut grass

b) A pool pumps out water at 700 gallons per minute

c) A culture of bacteria doubles every half hour

d) You lose $5 for every math question you miss

48. Which is the graph of the following function: 1( ) 22

f x x= − (F.IF.7, F.IF.7a)

a) b)

c) d)

Use the following function for questions 48-49

1( ) 22

f x x= −

49. The rate of change is _______________.

a) constant

b) variable

50. What happens to the end behavior on the right side of ( )f x ?

a) as x increases, f(x) increases towards infinity

b) as x increases, f(x) decreases towards negative infinity

c) there is no correlation between x and f(x)

−4 −3 −2 −1 1 2 3 4 5

−4

−3

−2

−1

1

2

3

4

x

y

−4 −3 −2 −1 1 2 3 4 5

−4

−3

−2

−1

1

2

3

4

x

y

−4 −3 −2 −1 1 2 3 4 5

−4

−3

−2

−1

1

2

3

4

x

y

−4 −3 −2 −1 1 2 3 4 5

−4

−3

−2

−1

1

2

3

4

x

y