Download Math 8 Unit 4 Functions

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Math 8 Unit 4 Functions Summative Assessment (Advanced)
1. Which relation below is a function? (MCC.8.F.1)
a. {(1, 2), (3, 5), (3, 8), (4, 9)}
b. {(-1, 3), (0, 7), (3, 7), (6, 6)}
c. {(2, 1), (2, 2), (2, 3), (2, 4)}
d. {(-8, 3), (3, -8), (5, 10), (5, 8)}
2. Tell whether the relation is a function. Explain why or why not. If the relation is not a function,
provide a counterexample. (MCC.8.F.1)
3. Tell whether the relation is a function. Explain why or why not. If the relation is not a function,
provide a counterexample. (MCC.8.F.1)
4. Tell whether the relation is a function. Explain why or why not. If the relation is not a function,
provide a counterexample. (MCC.8.F.1)
1
2
2
3
3
4
5. Tell whether the relation is a function. Explain why or why not. If the relation is not a function,
provide a counterexample. (MCC.8.F.1)
𝒚 = 𝟑𝒙 + 𝟐
6. Tell whether the relation is a function. Explain your yes or no answer. If the relation is not a
function, provide a counterexample. (MCC.8.F.1)
𝒚𝟐 = 𝒙
In problems 7-9 determine which function has a greater rate of change. Justify your answer.
(MCC.8.F.2)
7.
Function 1: y = 3x + 5
Function 2 : y = 5x + 3
8.
Function 1: (2, 2) (3, 3) (4, 4) (5, 5)
Function 2: y = x + 1
9.
Function 1:
Function 2:
x
y
-1 6
0
3
1
0
2
-3
10. Which of the following is a function? Justify your answer. (MCC.8.F.1)
A.
B.
C.
D.
x
1
1
2
x
2
1
2
x
1
2
3
x
1
1
1
y
2
3
4
y
2
3
4
y
3
3
3
y
2
3
4
11. Which mapping diagram is not a function? Justify your answer. (MCC.8.F.1)
A.
B.
C.
D.
1
2
1
1
2
2
1
1
1
1
2
2
2
12. Which Graph is a function? Justify your answer. (MCC.8.F.1)
a.
B.
C.
D.
13. Which equation is not a function? Justify your answer. (MCC.8.F.1)
A.
B.
C.
D.
𝑦 = |𝑥 + 4| − 3
𝑦 = 𝑥2 + 4
𝑦 = −3
1
𝑥=5
14. For each of the following situations, create a table and a graph to model the relationship. Then
describe the situation as increasing or decreasing, and linear or nonlinear.
a.
Mike has $25. He saves $11 each week.
x
y
b. Nettie has $2. She triples her money each week.
x
y
c. Paul has $100. He spends $5 each day.
x
y
For each of the following problems, complete the other representations for the situation.
16.
Table
x (days)
0
Make the Graph
y(meals)
0
1
3
2
6
3
9
4
12
What is the rate of change (slope)?
What is the start point?(constant)
What is the equation?
What is the story?
17.
x(
Fill in the table
)
y(
Graph
)
What is the rate of change (slope)?
What is the start point?(constant)
What is the equation?
What is the story?
Answer Key:
1. b
2. Yes, because each x(input) has one unique y(output).
3. No, because when you apply a vertical line there are two points that touch (vertical line test); there
are two x’s for more than one y (the x’s repeat). Counterexample: If the graph were turned pointing up
or down instead of to the left (rotated 90 degrees it would be a function)
4. No, because the 3 repeats in the domain [for (3,3) and (3,4)]. Counterexample: If you changed it to
(4,4) and (3,3) it would be a function.
5. Yes, because the constant is that it’s being multiplied by three every time
6. Yes, because each x only has one y. (It would be a curved line increasing from the origin.)
7. Function 2 because the rate of change (slope) is 5, which is greater than 3.
8. Neither, they are equal because the rate of change (slope) is 1 for each.
9. Function 1 is greater because the rate of change (slope) is -3, which is greater than 1.
10. c, because none of the x values repeat.
11. d, because the x values have more than one y value and you would get (1,1) and (1,2)
12. a, because it is a horizontal line none of the x values repeat
13. d, because all of the x values would be 5 (they would repeat, making a vertical line)
14. a) Table: (0,25) (1,36) (2,47) (3,58) (4,69); Graph: Slope of 11, y-intercept at (0,25). It is linear and it
is increasing
b) Table: (0,2) (1,6) (2,18) (3,54) (4,162); Graph: y-intercept at (0,2),. It is nonlinear (
increasing
) and it is
c) Table: (0,100) (1,95) (2, 90) (3,85) (4,80); Graph: Slope -5, y-intercept at (0,100). It is linear and it is
decreasing
16. Table: already done; Slope is 3, Starts at 0, Equation y=3x; Graph: Line with slope of 3 starting at the
origin; Story: You eat 3 meals every day
17. Table: x(seconds) and y(words)-possible answers for x: 0,1,2,3,4,5 and y:5,10,15,20,25,30 ; Slope is
5, Starts at 0, Equation y=5x; Graph: already done; Story: You can read 5 words each/per second