quantities and relationships end of topic test form a...–1 1 5. identify the function family of a...

QUANTITIES AND RELATIONSHIPS: End of Topic Test Form A • 5

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QUANTITIES AND RELATIONSHIPS

End of Topic Test Form AName Date

1. Brie knows there is a relationship between the grades on her math tests and the time she spends studying for those tests. Identify the independent quantity and the dependent quantity in this problem situation.

2. Consider each scenario. Analyze each graph and determine which of the provided scenarios it models. Explain your reasoning. Then for each graph, label the x- and y-axis with the appropriate quantity and unit of measure.

a. Test Score Arlene begins a test

with a possible total of 80 points. She loses 2 points for every question she answers incorrectly.

b. Piggy Bank Heath has 10 pennies in

his piggy bank initially. He doubles the number of pennies in his piggy bank each day for fi ve days.

c. Festival Cost It costs $5 to enter the

school’s Fall Festival and $0.50 per ticket purchased.

0 x

y

0 x

y

0 x

yGraph 1 Graph 2 Graph 3

IM1_AS_EoTA_M01_T01.indd 5IM1_AS_EoTA_M01_T01.indd 5 6/4/18 2:30 PM6/4/18 2:30 PM

6 • MODULE 1: Searching for Patterns


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3. Michael’s family was traveling to visit prospective colleges. They drove to the closest college that interested him, took a tour, and then drove to another college a little farther from home. The graph shown represents this situation.

a. Identify the domain and range.

b. Is the graph discrete or continuous?

c. Identify the maximum point and explain what it means in the problem situation.

d. Is the graph increasing, decreasing, both increasing and decreasing, or constant? Explain your reasoning.

1

120

240

360

480

600

0 2 3 4

Michael’s College Tour Trip

Time (hours)

Dis

tanc

e fr

om H

ome

(mile

s)

5 x

y




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4. Determine whether each relationship represents a function. Explain why or why not.

a. y

x

b. y

x

c. x y

22 100

22 50

0 0

2 50

d.

2

3

4

Domain Range

–1

1

5. Identify the function family of a graph that is made up of two straight lines, has an absolute maximum or absolute minimum, and is symmetric.

6. Classify each function as increasing, decreasing, or constant. Explain your reasoning.

a. f(x) 5 2 1 __ 2 x

b. f(x) 5 5x




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7. Classify each function as a linear function, a linear absolute value function, a quadratic function, or an exponential function. Explain your reasoning.

a. f(x) 5 3x 1 1

b. f(x) 5 5x2 2 20x 1 23

8. Determine whether each function has an absolute maximum or absolute minimum. If the graph has neither an absolute maximum nor an absolute minimum, write none.

a. f(x) 5 |x| 1 2

b. f(x) 5 0.2x

9. Sketch a graph of the given situation.

Evan is the quarterback for his school’s football team. In one of the pass routes he throws, the ball leaves his hand and is in the air for a few seconds. The ball reaches a maximum height of 12 feet off the ground. Then the ball lands in the receiver’s arms.

0Time (seconds)

Hei

ght o

f Bal

l (fe

et)

x

y




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10. Match each function to its graph. Explain your reasoning.

a. f(x) 5 2x2 1 4 b. f(x) 5 2x

c. f(x) 5 |x 2 1| d. f(x) 5 x 1 1

Graph A Graph B

−16 −8

−8

0 4 8 12 16

−16

−12

16

12

8

4

y

x

−4−12 −4

−16 −8

−8

0 4 8 12 16

−16

−12

16

12

8

4

y

x

−4−12 −4

Graph C Graph D

−16 −8

−8

0 4 8 12 16

−16

−12

16

12

8

4

y

x

−4−12 −4

−16 −8

−8

0 4 8 12 16

−16

−12

16

12

8

4

y

x

−4−12 −4




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11. Create an equation and sketch a graph of a function that is linear, continuous, and decreasing.

12. Create an equation and sketch a graph of a function that is quadratic, discrete, and has an absolute maximum.




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13. Write a scenario to match each graph.

a.

0 Time (hours)

Earn

ings

(dol

lars

)

x

y

b. Graph B

0 Speed (miles per hour)

Tim

e (h

ours

)

x

y

Graph A


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quantities and relationships end of topic test form a...–1 1 5. identify the function family of a...

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