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LINEAR FUNCTIONS: End of Topic Test Form A • 9

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End of Topic Test Form AName Date

1. Rewrite each explicit formula in function form.

a. an 5 19 2 7(n 2 1)

b. an 5 1.5 1 4.2(n 2 1)

2. A tree is currently 8 feet tall and grows 3 feet per year.

a. Model this scenario with an arithmetic sequence in explicit form.

b. Rewrite the explicit form of the sequence using function notation.

c. How tall will the tree be in 12 years?

3. Recall what you have learned about arithmetic sequences and linear functions to help you answer the following questions.

a. Can all arithmetic sequences be modeled by a linear function? If not, provide a counterexample.

b. Can all linear functions be modeled by an arithmetic sequence? If not, provide a counterexample.

c. Compare the domain of arithmetic sequences to the domain of linear functions.

4. Calculate the average rate of change for f(x).

–4 –2 2

2

–2

–4

4

6

8

4 x

y

0–6–8

–6

–8

6 8

f(x)

LINEAR FUNCTIONS

IM1_AS_EoTA_M02_T01.indd 9IM1_AS_EoTA_M02_T01.indd 9 5/31/18 8:32 AM5/31/18 8:32 AM

10 • MODULE 2: Exploring Constant Change

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LINEAR FUNCTIONS

5. Determine whether each table represents a linear function. For those that represent linear functions, write the function. For those that do not, explain why not.

a. x y

210 216

23 22

1 6

2 8

b. x y

23 28

22 26

0 1

1 2

6. A faucet leaks water at a constant rate. Tara places a measuring cup under the leak to catch the water. The table shows the number of milliliters of water in the cup at diff erent times.

Time (hours) Amount of Water (milliliters)

3.5 14

4 16

4.5 18

5 20

a. Determine the average rate of change for the problem situation. Be sure to include units.

b. Write a function to model the table of values.

c. Determine the amount of water in the cup after the faucet leaks at a constant rate for 12 hours.



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LINEAR FUNCTIONS

7. Gina has saved $420. She plans to spend $35 each month for music lessons. The function s(t) 5 235t 1 420 describes her savings, s, in dollars as a function of the time, t, in months.

a. Graph the function that describes Gina’s savings as a function of the time she works. Label the x{ and y{intercepts and explain what they mean in the problem situation.

b. Write the function you graphed in factored form.

c. Determine how much Gina will have left of her savings after 10 months.

8. Using the graph below, how many gallons of gas can be purchased for $15.80?

4

10

20

30

40

0 8 12 16Amount of Gasoline (gallons)

Cost

(dol

lars

)

x

y

9. Use the graph to determine when f(x) 5 5 and the value of f(5).

–4 –2 2

2

–2

–4

4

6

8

4 x

y

0–6–8

–6

–8

6 8



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LINEAR FUNCTIONS

10. For each of the following, a function has been given along with its graph. Perform the specifi ed transformation of the function and graph.

a. f(x) 5 3x 1 3 Graph: f(x) 2 3 Graph A

–4 –2 2

2

–2

–4

4

6

8

4 x

y

0–6–8

–6

–8

6 8

b. f(x) 5 x 1 7 Graph: 22f(x) Graph B

–4 –2 2

2

–2

–4

4

6

8

4 x

y

0–6–8

–6

–8

6 8

c. f(x) 5 2x 1 1 Graph: 2f(x) 1 3

Graph C

–4 –2 2

2

–2

–4

4

6

8

4 x

y

0–6–8

–6

–8

6 8



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LINEAR FUNCTIONS

11. Write the equation of a line that passes through the point (22, 6) and is parallel to the line that passes through the points (0, 24) and (3, 2).

12. Write the equation of a line that passes through the point (24, 25) and is perpendicular to a line that passes through the points (26, 8) and (10, 0).

13. Use the functions f(x) and g(x) to complete the comparison statements using <, >, or =.

x f(x)

23 20.5

22 0

21 0.5

0 1

–4 –2 2

2

–2

–4

4

6

8

4 x

y

0–6–8

–6

–8

6 8

a. f(23) g(23)

b. slope of f slope of g

c. y-intercept of f y-intercept of g



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LINEAR FUNCTIONS

14. Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.

0

Sara

x

y Ashton

Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.

a. Use what you know about Sara’s collection to determine the scale of each axis and interpret the origin on the graph.

b. Compare the slope and y-intercept for each function in terms of the quantities.


linear functions end of topic test form a - weebly

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