Unit 9 Test Name ___________________________

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1. Identify the function as linear or exponential: a)

x -2 -1 0 1 2

y 1 3 5 7 9

b)

x -2 -1 0 1 2

y 0.5 1 2 4 8

2. Fill the table and graph the function:

𝑦 =𝑥

2− 4

x -2 -1 0 1 2

y

3. Fill the table and graph the function: 𝑦 = 2 ⋅ (4)𝑥

x -2 -1 0 1 2

y

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4. A linear function is one by which the difference intervals does which of the following: a) Increases at a constant rate b) Decreases at a constant rate c) Stays the same d) None of the above

5. An exponential function is one whose interval does which of the following:

a) Grows quickly b) Grows by an equal factor c) Grows by an equal interval d) All of the above

6. The gym offers 3 membership plans.

Pay As You Go: $7 each time you work out Regular Deal: $48 per month plus $2.25 each time you work out Unlimited Deal: $120 per month for unlimited use What does the y-intercept of each function represent?

7. Compare the rate of change and the y-intercept for both functions. Based on this information,

which function would you choose? Function A: A rental store charges $50 to rent a steam cleaner and $3 for each additional hour. Function B:

Hours - x Total cost - f(x)

2 50

3 56

4 62

5 68

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8. Compare different characteristics of both functions by filling in the cells of the table:

𝑦 = 6 + 4𝑥 𝑦 = 6 ⋅ (4)𝑥

Type of Growth

Sequence Kind

Table Values

x y

-2

0

2

x y

-2

0

2

9. The first and fifth terms of a sequence are given. Fill in the missing numbers for an arithmetic sequence. Then fill in the numbers for a geometric sequence.

Arithmetic -12 -0.75

Geometric -12 -0.75

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10. Compare the rates of change of the given functions. Make a table of values and graph the both functions on the same coordinate plane. 𝑓(𝑥) = −(4)𝑥 + 1

𝑔(𝑥) = −4𝑥 − 4

x f(x) g(x)

-2

-1

0

1

2

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11. You have just been offered a part time work (study job) for all four years of college. They will

pay you a starting salary of $5000 with a raise of $500 per year.

a) Is the situation best modeled by a linear model or an exponential model? b) Write an equation that represents your salary after x years. c) Determine your salary after 2 years.

12. You have two options for your job salary.

Option A: Salary starts at $50,000. Salary grows by $1,000 per year. Option B: Salary starts at $40,000. Salary grows by 3% per year.

Which option will yield the higher salary in the long run? 13. Given 𝑓(𝑥) = 2𝑥2 − 3𝑥 and 𝑔(𝑥) = −5𝑥 + 7. Evaluate each of the following:

a) (𝑓 + 𝑔) (2) b) (𝑓 − 𝑔) (0)

14. Given 𝑓(𝑥) = −5𝑥2 + 4𝑥 and 𝑔(𝑥) = −2𝑥 + 8. Evaluate each of the following:

a) (𝑓 𝑔) (𝑥)

b) (𝑓

𝑔) (1)

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15. Let 𝑓(𝑥) = 2𝑥 + 3 and 𝑔(𝑥) = 3𝑥 − 2. Fill in the cells of the table.

x f g 𝑔 ∘ 𝑓

-2

-1

0

1

2

16. Using the functions below, answer on questions: 𝑓(𝑥) = 2𝑥

𝑔(𝑥) = √4𝑥

a) 𝑓(10) = ______ b) 𝑔(16) = ______

17. Using the functions below, answer on questions: ℎ(𝑥) = 𝑥3 − 5

𝑗(𝑥) =𝑥

2

a) ℎ(2) = ______ b) 𝑗(28) = ______

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18. Fill the table:

𝑓(𝑥) 𝑔(𝑥) (𝑓 ∘ 𝑔)(𝑥) Domain

(𝑓 ∘ 𝑔)(𝑥) (𝑔 ∘ 𝑓)(𝑥)

Domain (𝑔 ∘ 𝑓)(𝑥)

𝑥2 𝑥 + 3

1

𝑥 − 1 √𝑥

19. State the domain of each function below:

a) 𝑓(𝑥) = 𝑥2

b) 𝑔(𝑥) = √𝑥 − 5

c) ℎ(𝑥) = 5𝑥2 − √𝑥 − 2 20. Identify the initial amount and the change represented in each situation:

a) The amount of money in a savings account can be modeled by the function: 𝑓(𝑥) = 12 ⋅ (1.03)𝑥

b) The amount of a radioactive substance can be modeled by the function:

𝑟(𝑥) = 20 ⋅ (0.82)𝑥

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Answers:

1. a) Linear b) Exponential

2.

x -2 -1 0 1 2

y -5 -9/2 -4 -7/2 -3

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3.

x -2 -1 0 1 2

y 1/8 1/2 2 8 32

4.

c) Stays the same 5.

b) Grows by an equal factor 6. The y-intercept of each function represents how much money a user will spend by each

membership plan if he wouldn’t go to the gym at all. 7. If I would use a steam cleaner for more than 4 hours, I will use Function A. If I would use a steam

cleaner for less than 4 hours, I will use Function B. If I would use a steam cleaner for 4 hours, I can use either Function A or Function B, it will be the same amount.

Unit 9 Test Name ___________________________

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8.

𝑦 = 6 + 4𝑥 𝑦 = 6 ⋅ (4)𝑥

Type of Growth Linear Exponential

Sequence Kind Arithmetic Geometric

Table Values

x y

-2 -2

0 6

2 14

x y

-2 3/8

0 6

2 96

9.

Arithmetic -12 -9.1875 -6.375 -3.5625 -0.75

Geometric -12 -6 -3 -1.5 -0.75

10.

x 𝑓(𝑥) 𝑔(𝑥)

-2 0.9375 4

-1 0.75 0

0 0 -4

1 -3 -8

2 -15 -12

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11.

a) Linear model b) 𝑦 = 500𝑥 + 5000 c) After 2 years, your salary will be𝑦 = $6000.

12. Since the time is unlimited, eventually option B will result in a higher salary. 13.

a) (𝑓 + 𝑔) (2) = −1 b) (𝑓 − 𝑔) (0) = −7

14.

a) (𝑓𝑔)(𝑥) = 10𝑥3 − 48𝑥2 + 32𝑥

b) (𝑓

𝑔)(𝑥) = −

1

6

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15.

x f g 𝑔 ∘ 𝑓

-2 -1 -8 -5

-1 1 -5 1

0 3 -2 7

1 5 1 13

2 7 4 19

16.

a) 𝑓(10) = 20 b) 𝑔(16) = 8

17.

a) ℎ(2) = 3 b) 𝑗(28) = 14

18.

𝑓(𝑥) 𝑔(𝑥) (𝑓 ∘ 𝑔)(𝑥) Domain

(𝑓 ∘ 𝑔)(𝑥) (𝑔 ∘ 𝑓)(𝑥)

Domain (𝑔 ∘ 𝑓)(𝑥)

𝑥2 𝑥 + 3 𝑥2 + 6𝑥 + 9 (−∞, ∞) 𝑥2 + 3 (−∞, ∞)

1

𝑥 − 1 √𝑥

1

√𝑥 − 1 [0,1) ∪ (1, ∞)

1

√𝑥 − 1 (1, ∞)

19.

a) 𝐷: (−∞, ∞) b) 𝐷: [5, ∞) c) 𝐷: [2, ∞)

20.

a) 12 is the initial amount of money in the account and the interest rate is 3%. b) 20 represents the amount of the substance at the beginning. The decay rate is 18%.