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Unit 3: Modeling with Linear Functions - Practice Test
Questions 1 – 4: Lesson 1: Proving Linearity
1. Which account balance would best be modeled by a linear function?
a. a loan with no interest being paid at $300 per month
b. a loan with a 3% monthly interest rate being paid at $300 per month
c. a savings account earning 3% interest per month with no deposits made
d. a checking account with a balance that increases one month and decreases the next month
2. Which table of values represents a linear function?
a.
x
f(x)
4
12
5
15
6
18.75
7
23.4375
b.
x
f(x)
4
15
7
24
9
30
15
48
c.
x
1
2
3
4
f(x)
10
11
10
7
d.
x
-1
0
1
2
f(x)
3.375
4.5
6
8
3. The data given below is the population, P, of Mexico (in millions) based on the year, y.
y
P
1980 67.38
1981 69.13
1982 70.93
1983 72.77
1984 74.67
1985 76.61
1986 78.60
Would a linear function be reasonable to model this data? Why/why not?
4. Studies have shown that a person’s body metabolizes alcohol at a constant rate. So, for every 40
minutes, a person’s body metabolizes 0.01% of alcohol in their blood. In the United States, a
person is considered legally impaired if their blood alcohol content (BAC) is 0.08% or higher
(about 4 drinks for a 180 lb. male).
Jack is 17 years old and has had 8 drinks and has a BAC of 0.17% resulting in slurred speech,
staggering, and poor motor control. The legal BAC limit for a driver under 21 is 0%. If Jack stops
drinking now, how long will he have to wait at the party before he can drive himself home?
Unit 3: Modeling with Linear Functions - Practice Test
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Questions 5 – 9: Lesson 2: Arithmetic Sequences
5. The height of the water level in a tank is 200 inches. The water level increases at a constant rate
of 3 inches every day.
H(t)= height of the water level after t days.
H(0)=200
Enter the function for t ≥ 1 that describes the height of the water level, H(t), on the tth day in
terms of the height of the water level at the same time on the previous day, H(t − 1).
6. Consider this function in explicit form.
f(n) = 3n – 4; n ≥ 1
Select the equivalent recursive function.
a. f(1) = -1
f(n) = f(n – 1) + 3; n ≥ 2
b. f(1) = -1
f(n) = 3f(n – 1); n ≥ 2
c. f(0) = -4
f(n) = 3f(n – 1); n ≥ 2
d. f(0) = -4
f(n) = f(n – 1) + 3; n ≥ 2
7. Consider this function in recursive form.
f(1) = -3
f(n) = f(n – 1) + 3; n ≥ 2
Select the equivalent explicit function for n ≥ 1.
a. f(n) = 3(n – 1)
b. f(n) = -3(n – 1)
c. f(n) = n + 3
d. f(n) = 3n – 6
8. What is the 4th term in the sequence modeled by the recursive formula
NEXT = 2 • NOW + 5 if the first term is equal to 5?
a.
b.
c.
d.
15
35
60
75
9. A sequence is defined by the function f(n) = f(n – 1) + 5 where n represents the number
of the term for n ≥ 2 and f(1) = -4What are the first four terms of the sequence?
Unit 3: Modeling with Linear Functions - Practice Test
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Question 10: Lesson 3: Analyzing Functions using Different Representations
10. Suppose that g(x) = -1.5x – 1.5
a. Find and equation for h(x) such that h(x) = g(x) – 3
b. Sketch a graph of g(x) and h(x)
Questions 11 – 12: Lesson 4: Solving Simultaneous Linear Equations Algebraically
11. (NC DPI) Lucy and Barbara began saving money the same week. The table below shows
the models for the amount of money Lucy and Barbara had saved after x weeks.
Lucy’s Savings
F(x) = 10x + 5
Barbara’s Savings G(x) = 7.5x + 25
After how many weeks will Lucy and Barbara have the same amount of money saved?
A 1.1 weeks
B 1.7 weeks
C 8 weeks
D 12 weeks
12. The bill for a lunch of three hamburgers and two drinks is $9.67. The bill for a lunch of six
hamburgers and seven drinks is $22.19. What is the total cost of one hamburger and one drink?
Questions 13: Lesson 5: Solving Simultaneous Linear Equations Graphically
13. This graph shows linear equations y = f(x) and y = g(x).
Find the solution to the equation f(x) – g(x) = 0
Unit 3: Modeling with Linear Functions - Practice Test
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Questions 14 – 15: Lesson 6: Solve Systems of Linear Inequalities
14. The graph shown represents the set of ordered pairs that are solutions to an inequality
What is the inequality that represents the solution set shown by the graph?
15. Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice
cream shop for $8 per hour. Leah cannot work more than a total of 20 hours per month. Let x
represent the number of hours Leah works at the ice cream shop.
A: Graph the solution set of the system of linear inequalities in the coordinate plane.
B: Which pairs (x, y) represent hours that Leah could work to meet the given conditions?
(4, 15) (5, 12) (10, 9) (15, 5) (19, 1)
Unit 3: Modeling with Linear Functions - Practice Test
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Solutions:
1. A
2. B
3. Yes, it would be reasonable since the rate of change is almost the same between each pair of
years
4. 11 1/3 hours
5. H(t ) = H(t – 1) + 3
6. A
7. D
8. D
9. -4, 1, 6, 11
10. Solution:
a. h(x) = -1.5x – 4.5
b. https://www.desmos.com/calculator/5mr0gm7pn2
11. C
12. Burger: $2.59 Drink: $0.95 – Total: $3.54
13. Give credit if student gives any point between -4.2 to -4
14. y ≥ -x + 1
15. Part A:
Part B: (4, 15), (5, 12), and (10, 9)
Unit 3: Modeling with Linear Functions - Practice Test
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