G8 U6 Assessment
Name: ______________________________
Date:________________
Grade 8 Unit 6 Assessment Modeling Relationships with Functions 1. A rental car company charges a non-refundable deposit and a daily rate. Sasha rented a car for four days and was charged $190. Marlene rented a car for five days and was charged $225. Find the cost of the non-refundable deposit A. $45 B. $35 C. $47.50 D. $50 2. Find the rate of change in the graph of the function 12 10 8 6 4 2 0 0
2
4
6
8
10
.
A. −1.25 B. 10 C. −0.8 D. 8 Copyright © Swun Math Grade 8 Unit 6 Assessment, Page 1
3. Thirty-two degrees Fahrenheit is zero degrees Celsius, and 212℉ is 100℃. If the temperature dropped by 10℉, how much would the change be in degrees Celsius? A. −18℃ B. −18.9℃ C. −5.6℃ D. −4.7℃ 4. Find the rate of change in the function below x -5 0 3 7 10 f(x) 22 10 2.8 -6.8 -14 A. 10 B. 2.4 C. −1.4 D. −2.4
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5. Barney is about to buy several special calligraphy pens for $6.50 each. If he buys p pens, write a function for the amount of change, c, he will receive from a $50 bill. A. 𝐶 (𝑝) = 6.5𝑝 + 50. B. 𝑃(𝑐) = 50 − 6.5𝑐 C. 𝐶 (𝑝) = 6.5𝑝 − 50 D. 𝐶 (𝑝) = −6.5𝑝 + 50
6. Which graphs show a function that only increases in value when 𝑥 ≥ 0? Select all that apply. 8 6 4 I 2 0 -3 -2 -1 -2 0 1 2 3 -4 -6 -8
4
2
3
II
2 1
III
2
IV
1 -2
1 0 -2
-1
0 -1 0 -1
0 0
1
2
-2
A. I
B. II
C. III
D. IV
-1
0
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1
2
-2
1
2
7. Scott recently remembered an account that he used years ago and never closed. He starts depositing $100 per month, as the graph shows. How much was in the account when he started depositing? 600 500 400 300 200 100 0
-1
0
1
2
3
A. $250 B. $300 C. $200 D. $150 8. Jenny’s house was worth $198,000 in 2009 and $226,000 in 2013. At this rate how much will it be worth in 2020? A. $275,000 B. $254,000 C. $395,500 D. $226,800 Copyright © Swun Math Grade 8 Unit 6 Assessment, Page 4
9. Write a function that relates the values in the table below. x f(x)
-2 -5
4 10
10 25
A. 𝑓(𝑥 ) = 0.4𝑥 − 5 5
5
2
2
B. 𝑓(𝑥 ) = 𝑥 + C. 𝑓 (𝑥 ) = 2.5𝑥
D. 𝑓(𝑥 ) = 2𝑥 + 2 10. The water container below is filled by a small hose running at a constant rate. Which graph relates time on the horizontal axis and water level on the vertical axis? A
f(x)
B
f(x)
x
x
C
f(x)
D
f(x)
x
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x
11. Which linear function has a negative initial value but a positive rate of change? 5 4 3 2 1 0 -1 0 -2 -3 -4 -5
A B 1
C
2
D
A. Line A
B. Line B
C. Line C
D. Line D
12. The chart below shows the relationship between driving speed, s, and braking distance, d. s 20 30 40 50 60 d 14 31 58 90 130
Check if each statement about the relationship is correct. A. The initial value would be zero. Y N B. The function is linear.
Y
N
C. The function is increasing over the range shown.
Y
N
D. The rate of change is constant.
Y
N
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13. A large cheese pizza costs $9 plus $1.75 for each topping. Write a function equation relates the cost and the number of toppings. Answer: ________________________ 14. The graph below relates time and the height of a person above the center of the Ferris wheel he is riding.
Determine if the following statements are true. A. The graph shows two complete revolutions of the wheel.
T
F
B. The rate of change is constant.
T
F
C. The height is increasing twice on the graph.
T
F
T
F
D. The height is decreasing twice on the graph.
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15. Thirty-two degrees Fahrenheit is zero degrees Celsius, and 212℉ is 100℃. Write a function equation in which F depends on C.
Answer:__________________ 16. Sketch a graph of a function that is increasing when 𝑥 < 0, the 𝑓(0) = 4, and the function is decreasing when 𝑥 > 0.
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Date:________________
Grade 8 Unit 6 Assessment Modeling Relationships with Functions 1. A rental car company charges a non-refundable deposit and a daily rate. Sasha rented a car for four days and was charged $190. Marlene rented a car for five days and was charged $225. Find the cost of the non-refundable deposit A. $45 B. $35 C. $47.50 D. $50 2. Find the rate of change in the graph of the function 12 10 8 6 4 2 0 0
2
4
6
8
10
.
A. −1.25 B. 10 C. −0.8 D. 8 Copyright © Swun Math Grade 8 Unit 6 Assessment, Page 1
3. Thirty-two degrees Fahrenheit is zero degrees Celsius, and 212℉ is 100℃. If the temperature dropped by 10℉, how much would the change be in degrees Celsius? A. −18℃ B. −18.9℃ C. −5.6℃ D. −4.7℃ 4. Find the rate of change in the function below x -5 0 3 7 10 f(x) 22 10 2.8 -6.8 -14 A. 10 B. 2.4 C. −1.4 D. −2.4
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5. Barney is about to buy several special calligraphy pens for $6.50 each. If he buys p pens, write a function for the amount of change, c, he will receive from a $50 bill. A. 𝐶 (𝑝) = 6.5𝑝 + 50. B. 𝑃(𝑐) = 50 − 6.5𝑐 C. 𝐶 (𝑝) = 6.5𝑝 − 50 D. 𝐶 (𝑝) = −6.5𝑝 + 50
6. Which graphs show a function that only increases in value when 𝑥 ≥ 0? Select all that apply. 8 6 4 I 2 0 -3 -2 -1 -2 0 1 2 3 -4 -6 -8
4
2
3
II
2 1
III
2
IV
1 -2
1 0 -2
-1
0 -1 0 -1
0 0
1
2
-2
A. I
B. II
C. III
D. IV
-1
0
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1
2
-2
1
2
7. Scott recently remembered an account that he used years ago and never closed. He starts depositing $100 per month, as the graph shows. How much was in the account when he started depositing? 600 500 400 300 200 100 0
-1
0
1
2
3
A. $250 B. $300 C. $200 D. $150 8. Jenny’s house was worth $198,000 in 2009 and $226,000 in 2013. At this rate how much will it be worth in 2020? A. $275,000 B. $254,000 C. $395,500 D. $226,800 Copyright © Swun Math Grade 8 Unit 6 Assessment, Page 4
9. Write a function that relates the values in the table below. x f(x)
-2 -5
4 10
10 25
A. 𝑓(𝑥 ) = 0.4𝑥 − 5 5
5
2
2
B. 𝑓(𝑥 ) = 𝑥 + C. 𝑓 (𝑥 ) = 2.5𝑥
D. 𝑓(𝑥 ) = 2𝑥 + 2 10. The water container below is filled by a small hose running at a constant rate. Which graph relates time on the horizontal axis and water level on the vertical axis? A
f(x)
B
f(x)
x
x
C
f(x)
D
f(x)
x
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x
11. Which linear function has a negative initial value but a positive rate of change? 5 4 3 2 1 0 -1 0 -2 -3 -4 -5
A B 1
C
2
D
A. Line A
B. Line B
C. Line C
D. Line D
12. The chart below shows the relationship between driving speed, s, and braking distance, d. s 20 30 40 50 60 d 14 31 58 90 130
Check if each statement about the relationship is correct. A. The initial value would be zero. Y N B. The function is linear.
Y
N
C. The function is increasing over the range shown.
Y
N
D. The rate of change is constant.
Y
N
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13. A large cheese pizza costs $9 plus $1.75 for each topping. Write a function equation relates the cost and the number of toppings. Answer: ________________________ 14. The graph below relates time and the height of a person above the center of the Ferris wheel he is riding.
Determine if the following statements are true. A. The graph shows two complete revolutions of the wheel.
T
F
B. The rate of change is constant.
T
F
C. The height is increasing twice on the graph.
T
F
T
F
D. The height is decreasing twice on the graph.
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15. Thirty-two degrees Fahrenheit is zero degrees Celsius, and 212℉ is 100℃. Write a function equation in which F depends on C.
Answer:__________________ 16. Sketch a graph of a function that is increasing when 𝑥 < 0, the 𝑓(0) = 4, and the function is decreasing when 𝑥 > 0.
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