AnswersPre-Algebra A-CRUnit Test

Introduction to Functions Answers

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Which statement describes how to determine if a relation given in a table is a function?

A
If none of the output values are repeated, the relation is a function.
B
If none of the input values are repeated, the relation is a function.
C
If any of the input values are equal to the output values, the relation is a function.
D
If all the output values are paired with the same input value, the relation is a function.
2
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Hal, Zelda, Maya, and Jason each recorded the height and age of five classmates. They used the data to create the tables below. In which student’s data can height be considered a function of age?

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A
Hal
B
Zelda
C
Maya
D
Jason
3

A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items?

A
y squared = 4 x squared minus 100
Option A
B
y = negative x squared + 50 x minus 300
Option B
C
x = negative y squared minus 400
Option C
D
x squared = negative 6 y squared + 200
Option D
4

Asha found that a vertical line intersects the graph of at two points. What can Asha conclude about ?

Question illustration
A
The graph passes the vertical line test and is a function.
B
The graph is not a function because it fails the vertical line test.
C
The graph shows a straight-line relationship between x and y.
D
The graph curves in a U-shape and always opens upward.
5

The equation below models the height in feet, h, of a softball t seconds after it is hit by a batter.Why is the height of the ball a function of time?

Question illustration
A
Each value of time is associated with exactly one height.
B
Each height of the ball is associated with exactly one moment in time.
C
There is exactly one time at which the maximum height is attained.
D
There is a maximum and minimum height that the ball can reach.
6

The graph below models the value of a $20,000 car t years after it was purchased. Value of CarWhich statement best describes why the value of the car is a function of the number of years since it was purchased?

Question illustration
A
Each car value, y, is associated with exactly one time, t.
B
Each time, t, is associated with exactly one car value, y.
C
The rate at which the car decreases in value is not constant.
D
There is no time, t, at which the value of the car is 0.
7

Which relation is a function of x?

A
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 2, 2, 3. Column 2 is labeled y with entries 7, negative 9, 8, negative 4.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 8, negative 8, 1, 1. Column 2 is labeled y with entries negative 9, 2, negative 9, 2.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 5, negative 5, negative 5. Column 2 is labeled y with entries 1, 7, negative 9, 2.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 2, 4, 7. Column 2 is labeled y with entries negative 1, 5, 0, negative 1.
Option D
8

Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes. Is the number of gallons of water in the bathtub a function of time?

Question illustration
A
Yes because each t value is paired with exactly one number of gallons.
B
Yes because the number of gallons is bounded between y = 0 and y = 36.
C
No because each number of gallons is paired with more than one t value.
D
No because from t = 5 to t = 20 the number of gallons of water is constant.
9

At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?

A
It is a function because at any given time the oven was exactly one temperature.
B
It is a function because the oven temperature was the same at different times.
C
It is not a function because at any given time the oven was exactly one temperature.
D
It is not a function because the oven temperature was the same at different times.
10

Which graph is a function of x?

A
On a coordinate plane, a vertical line is at x = negative 3.
Option A
B
On a coordinate plane, a v-shaped graph opens up.
Option B
C
On a coordinate plane, a parabola opens to the right.
Option C
D
On a coordinate plane, one curve opens to the left and another curve opens to the right.
Option D

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