Unit 4: Functions

Multiple Choice

1. Describe the relationship shown in the table of values.

• A. Relation only

• B. Function only

• C. Relation and function

• D. Neither relation nor function

Multiple Choice

2. Which of the following sets of ordered pairs represents a function?

• A. (2, 3), (6, 9), (10, 12), (2, -3)

• B. (-9, 4), (-2, 10), (-2, 12), (0, 6)

• C. (1, 2), (4, 9), (10, 22), (15, 7)

• D. (0, 1), (0, 2), (0, 3), (0, 4)

Multiple Choice

3. Which graph DOES NOT represent a function?

Multiple Choice

4. Which of the following relations does NOT represent a function?

• A. {(5, 8), (10, 2), (12, -2), (15, -5)}

• B. 𝑦= 12𝑥+8

• C. Multiplying each input by 10 to produce an output

Multiple Choice

5. Choose the best description of the relation shown below:

{(2,10),(4,15),(6,20),(8,25)}

• A. The relation is a function because every input has exactly one output

• B. The relation is a function because every output has exactly one input

• C. The relation is not a function because every input is different

• D. It is impossible to tell if the relation is a function without knowing more coordinates.

Multiple Choice

6. Which equation shown below shows a linear relationship?

• A. $$𝑦=3𝑥+4$$

• B. $$𝑦=\frac{1}{2}𝑥^2-1$$

• C. $$2𝑥^2+𝑦=5$$

• D. $$𝑦=\frac{2}{x}$$

Multiple Choice

7. Which graph shows a linear relationship?

Multiple Choice

8. Choose the best description of the graph shown on the left.

• A. Linear because each section of the graph is a different straight line segment.

• B. Nonlinear because each segment has a different slope.

• C. Both linear and nonlinear because it is made up of straight line segments but is not a complete straight line.

• D. Neither linear nor nonlinear because it is made up of straight line segments but is not a complete straight line.

Multiple Choice

9. Which table shows nonlinear relationship?

Multiple Choice

10. Which equation represents the table?

• A. 𝑦=18𝑥+3

• B. 𝑦=3𝑥+18

• C. 𝑦= −3𝑥+18

• D. 𝑦= 13𝑥+18

Multiple Choice

11. Which equation represents the graph?

• A. $$𝑦=4𝑥−2$$

• B. $$𝑦=\frac{1}{2}𝑥+4$$

• C. $$𝑦=−2𝑥+4$$

• D. $$𝑦=-\frac{1}{2}𝑥+4$$

Multiple Choice

12. Which equation represents a line passing through the points (2, 5) and (4, 10)?

• A. $$𝑦=\frac{5}{2}𝑥$$

• B. $$𝑦=\frac{2}{5}𝑥$$

• C. $$𝑦=5𝑥+2$$

• D. $$𝑦=2𝑥+5$$

Multiple Choice

13. David’s allowance is $5 every week, plus $2 for each extra chore he does. Which equation shows his total allowance (A) every week, depending on the number of extra chores (c) he completes?

• A. $$𝐴=5𝑐+2$$

• B. $$𝐴=2𝑐+5$$

• C. $$𝐴=7𝑐$$

• D. $$𝐴=2+5$$

Multiple Choice

14. Compare the equation in Item 1 with the graph in Item 2.

• A. Items 1 and 2 have the same rate of change, and the same y-intercepts.

• B. Items 1 and 2 have the same rate of change, but different y-intercepts.

• C. Items 1 and 2 have different rates of change, but the same y-intercepts.

• D. Items 1 and 2 have the different rates of change, and different y-intercepts.

Multiple Choice

15. Consider the table of values and the graph to the left. Choose the statement below that best compares the two.

• A. The table has an increasing rate of change while the graph has a decreasing rate of change; the graph and the table have the same y-intercepts.

• B. Both the table and graph have increasing rates of change; The y-intercept of the graph is greater than that of the table.

• C. Both the table and graph have decreasing rates of change; The y-intercept of the table is greater than that of the graph.

• D. The table has a decreasing rate of change while the graph has an increasing rate of change; The y-intercept of the graph is greater than that of the table.

Multiple Choice

16. Consider the table of values and the equation to the left. Choose the statement that best compares the two.

• A. The table and equation have the same slope and the same y-intercepts.

• B. The table and the equation have the same slope, but different y-intercepts.

• C. The table and the equation have different slopes and different y-intercepts.

• D. The table and the equation have different slopes, but the same y-intercept.

Multiple Choice

17. Compare the equation and the graph. Choose the statement below that best describes the functions:

• A. The difference between the y-intercepts is 2.

• B. The difference between the y-intercepts is 1.

• C. The y-intercepts are equal

• D. The rates of change are equal

Multiple Choice

18. The graph below show’s Maggie’s distance from home. Which scenario could be a possible explanation for the path shown by the graph?

• A. Maggie starts at home and walks down a hill to her friend’s house.

• B. Maggie starts at her friend’s house and walks straight home.

• C. Maggie starts at home and walks south-east.

• D. Maggie starts at her friend’s house, passes her home and goes to the store.

Multiple Choice

19. Isaac is attempting to inflate a large beach ball. The graph below shows the amount of air in the beach ball over a period of time. Between which points does it show that Isaac had to take a break from inflating the beach ball?

• A. $$\overline{AB}\ ,\ \overline{CD\ }\ \&\ \ \overline{EF}$$

• B. $$\overline{BC},\ \overline{DE},\ \&\ \overline{FG}$$

• C. $$\overline{FG}$$ only

• D. $$\overline{EG}$$ only

Multiple Choice

20. Between which points was he inflating the beach ball the fastest?

• A. $$\overline{AB}$$

• B. $$\overline{BC}$$

• C. $$\overline{CD}$$

• D. $$\overline{EF}$$

Multiple Choice

21. Jordan is training to run a marathon. He can already run seven miles without stopping. Each week he is hoping to increase the amount he can run by at least ½ a mile. An equation of the situation is shown below. Interpret the y-intercept.

• A. The y-intercept represents the total number of miles Jordan wants to be able to run.

• B. The y-intercept represents the number of miles Jordan wants to add to his run each week.

• C. The y-intercept represents the number of miles Jordan can run at the beginning of his training.

• D. The y-intercept represents the total weeks he will have to train to reach his goal.

Multiple Choice

22. A study was done to investigate the relationship between a between eating sugary snacks and a test that measures a student’s memory and attention. The correlating linear model is shown below, where x represents the number of sugary snacks a student ate, and y represents the student’s test score. Interpret the rate of change (slope).

• A. Eating zero sugary snacks is associated with a loss of five points on the test.

• B. Each additional sugary snack eaten is associated with a loss of five points on the test.

• C. An additional five sugary snacks is associated with a loss of five points on the test.

• D. Not enough information is provided to interpret the slope.

Multiple Choice

23. The graph below shows the cost of a particular taxi cab service in Chicago. Interpret the initial value and the rate of change for the graph.

• A. The taxi charges $2 to enter the cab and an additional $2 for every mile traveled.

• B. The taxi charges $4 to enter the cab and an additional $1 for every mile traveled.

• C. The taxi charges $4 to enter the cab and an additional $2 for every mile traveled.

• D. The taxi charges $0 to enter the cab and an additional $2 for every mile traveled.

Multiple Choice

24. Luis worked at the town pet store and was in charge of draining and cleaning the fish tanks. He decided to record the amount of water in the tank and the time it took to drain the tank. Luis’ data is shown in the table below. Interpret the initial value and the rate of change.

• A. The tank started with 60 gallons and drained at a rate of 5 gallons per minute.

• B. The tank started with 60 gallons and drained in 10 minutes.

• C. The tank started with 50 gallons and drained at a rate of 10 gallons per minute.

• D. The tank started with 60 gallons and drained at a rate of 10 gallons per minute.

Multiple Choice

25. Julie planted sunflowers in her garden. She was curious about how fast they grow so she kept a weekly log of their height. Once the sunflowers were full grown, Julie analyzed her data and calculated the equation below to represent the (H) height, in centimeters, of her sunflowers, depending how many (W) weeks had passed after planting.

Interpret the y-intercept.

• A. The y-intercept in this situation means that each sunflower was 5 cm tall when planted.

• B. The y-intercept in this situation means that each sunflower was 24 cm tall when they were fully grown.

• C. The y-intercept in this situation means that each sunflower grew 24 cm each week.

• D. The y-intercept in this situation means that each sunflower grew 29 cm each week.