AnswersPre-Algebra - MA3119 A Distance LearningSolving Equations with Rational Numbers

Introduction to Functions Answers

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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
2
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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
3

The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation . Which statement best describes if the relation (c, f) is a function?

Question illustration
A
It is a function because –40°C is paired with –40°F.
B
It is a function because every Celsius temperature is associated with only one Fahrenheit temperature.
C
It is not a function because 0°C is not paired with 0°F.
D
It is not a function because some Celsius temperatures cannot be associated with a Fahrenheit temperature.
4

The graph below displays the wrist circumferences and heights of six students in Alyssa’s classroom. Is the height of these students a function of their wrist circumference?

Question illustration
A
Yes because as wrist circumference increases height also increases.
B
Yes because a line can be fit to these data to predict other pairings.
C
No because the height of 151 cm is paired with two wrist circumferences.
D
No because the wrist circumference of 16 cm is paired with two heights.
5

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

Question illustration
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.
6

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.
7

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)
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

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.
10

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

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