AnswersGA-8th Grade MathematicsUnit Test

Introduction to Functions Answers

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1
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Which statement best illustrates using the vertical line test to determine if the graph below is a function of x?

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A
The graph is not a function of x because the line x = 0 intersects the graph at two points.
B
The graph is a function of x because the line x = 5 does not intersect the graph.
C
The graph is not a function of x because the line y = 0 intersects the graph at two points.
D
The graph is a function of x because the line y = 5 does not intersect the graph.
2
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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.
3

The table below lists some of the characteristics of the houses on Katrina’s street.Characteristics of Homes For Sale on Katrina’s StreetBedroomsAcres of landSale priceAppraised valueProperty tax 20.17$230,000$200,000$1,22020.20$210,000$220,000$1,23230.20$275,000$250,000$1,40040.24$275,000$275,000$1,54040.52$360,000$310,000$1,73640.75$350,000$320,000$1,79251.23$375,000$350,000$1,960Which relationship describes a function?

A
(bedrooms, sale price)
B
(acres of land, appraised value)
C
(sale price, bedrooms)
D
(appraised value, property tax)
4

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.
5

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?

Question illustration
A
Hal
B
Zelda
C
Maya
D
Jason
6

Which statement is a correct interpretation of the vertical line test?

A
If only one vertical line intersects the graph at exactly one point, the graph represents a function.
B
If only one vertical line intersects the graph at exactly one point, the graph does not represent a function.
C
If any vertical line can intersect the graph at more than one point, the graph represents a function.
D
If any vertical line can intersect the graph at more than one point, the graph does not represent a function.
7

Removing which ordered pair from the table would make the relation a function of x? xy1747224139

A
(1, 7)
B
(2, 2)
C
(3, 9)
D
(4, 1)
8

If the relationships below are given in the form (input, output), which pairing always describes a function?

A
(number of doors in a car, number of cup holders in the car)
B
(height of a building in feet, height of the building in inches)
C
(beverage charge on a bill, total meal charge on the bill)
D
(distance from home during a trip, time elapsed during the trip)
9

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
10

Removing which point from the coordinate plane would make the graph a function of x?

Question illustration
A
(–4, 3)
B
(–2, 1)
C
(0, 4)
D
(1, 1)
11

Which equation is a function of x?

A
x = 5
B
x = y squared + 9
Option B
C
x squared = y
Option C
D
x squared = y squared + 16
Option D
12

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.
13

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
14

Lorraine writes the equation shown.She wants to describe the equation using the term relation and the term function.The equation represents

Question illustration
A
a relation and a function
B
a relation but not a function
C
a function but not a relation
D
neither a relation nor a function
15

The chart below lists the original and sale prices of items at a clothing store.Clothing PricesOriginal priceSale price$7.99$5.59$10.99$7.69$12.99$9.09$15.99$11.19$24.99$17.49$29.99$20.99Which statement best describes why the sale price is a function of the original price?

A
As the original price increases, the sale price also increases.
B
The sale price is always less than the original price.
C
For every original price, there is exactly one sale price.
D
The sales price is never less than zero.

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