AnswersMathematics 8Input-Output Relationships

Input-Output Relationships — Test Answers

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1
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Which is the best description for the given graph?

A
The graph increases everywhere.
B
The graph decreases everywhere.
C
The graph increases, then decreases.
D
The graph remains constant.
2
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Which label corresponds to the segment showing the balloon descending but not landing?

A
cap A
B
cap b
C
cap c
D
cap d
3

What is the rate of change of the function?

A
negative 1 half
B
negative 2
C
2
D
1 half
4

Jordana drew the given function. Which statement correctly explains whether or not her function is linear?

A
It is linear because it does not have a constant rate of change.
B
It is not linear because it has a constant rate of change.
C
It is linear because it has a constant rate of change.
D
It is not linear because it does not have a constant rate of change.
5

Which statement best describes the relation (package number, price)?

A
It is not a function because each package number has two different prices.
B
It is not a function because there are two different packages available for $180.
C
It is a function because weekend packages are always $50 more than weekday packages.
D
It is a function because there is a price given for every package.
6

Which equation represents the graph?

A
y is equal to negative x minus 10
B
y is equal to 10 minus x
C
y is equal to x minus 10
D
y is equal to 10 plus x
7

Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y -values as 7 minus 1 is equal to 6 , 17 minus 7 is equal to 10 , and 31 minus 17 is equal to 14 Then he concluded that since the differences of 6 , 10 , and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake?

A
He determined that the differences of 6 , 10 , and 14 are increasing by 4 each time.
B
He concluded that the function has a constant rate of change.
C
He found the differences in the y -values as 7 minus 1 is equal to 6 , 17 minus 7 is equal to 10 , and 31 minus 17 is equal to 14 .
D
He reasoned that a function that has a constant rate of change is linear.
8

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

A
open paren 0 comma 4 close paren
B
open paren negative 4 comma 3 close paren
C
open paren negative 2 comma 1 close paren
D
(1, 1)
9

Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be open paren negative 1 comma negative 4 close paren , open paren 0 comma negative 3 close paren , and open paren 2 comma 5 close paren Next, she determined the rate of change between the points open paren negative 1 comma negative 4 close paren and open paren 0 comma negative 3 close paren to be the fraction with numerator negative 3 minus negative 4 and denominator 0 minus negative 1 is equal to 1 over 1 is equal to 1 and the rate of change between the points open paren 0 comma negative 3 close paren and open paren 2 comma 5 close paren to be the fraction with numerator 5 minus negative 3 and denominator 2 minus 0 is equal to 8 halves is equal to 4 Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?

A
The expressions the fraction with numerator negative 3 minus negative 4 and denominator 0 minus negative 1 and the fraction with numerator negative 3 minus negative 5 and denominator 2 minus 0 both equal 1 .
B
She miscalculated the rates of change.
C
Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.
D
The points open paren negative 1 comma negative 4 close paren , open paren 0 comma negative 3 close paren , and open paren 2 comma 5 close paren are not all on the graph.
10

How does the graph change between point cap A and point cap b ?

A
The graph increases, then decreases.
B
The graph increases.
C
The graph remains constant.
D
The graph decreases.
11

Which equation represents the graph?

A
y is equal to 1 third x
B
y is equal to 3 x
C
y is equal to x minus 3
D
y is equal to x plus 3
12

How does the graph change between point cap A and point cap c ?

A
The graph decreases, then remains constant.
B
The graph increases, then remains constant.
C
The graph increases, then decreases.
D
The graph decreases, then increases.
13

Which describes the pattern of the data in the graph?

A
The water level increases by a factor of 1 half each hour.
B
The water level increases by 2 inches each hour.
C
The water level increases by 1 inch each hour.
D
The water level increases by a factor of 2 each hour.
14

Is the function in the graph non-linear?

A
Yes, because it does not have a constant rate of change.
B
No, because it does not have a constant rate of change.
C
Yes, because it has a constant rate of change.
D
No, because it has a constant rate of change.
15

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

A
open paren 1 comma 7 close paren
B
open paren 3 comma 9 close paren
C
open paren 2 comma 2 close paren
D
open paren 4 comma 1 close paren
16

Which equation is a function of x ?

A
x squared is equal to y squared plus 16
B
x is equal to y squared plus 9
C
x is equal to 5
D
x squared is equal to y
17

The table shows the number of tickets sold and the profit made at a fundraiser. Tickets Sold Profit 2 $18 4 $36 6 $54 8 $72 Which describes the relationship between the number of tickets sold and the profit?

A
Each ticket sold yields $16 of profit.
B
Each ticket sold yields $8 of profit.
C
Each ticket sold yields $9 of profit.
D
Each ticket sold yields $18 of profit.
18

On the way to her babysitting job, Mary rode her bike for the first mile. She stopped at a traffic light and waited a few minutes for the traffic light to turn green. She then walked her bike across the street and up a short steep hill. Finally, she rode the bike at a constant speed for one more mile. If Mary created a graph of her time and distance, which statement describes the part of her graph that would show no change in distance?

A
Mary stopped and waited for the traffic light to turn green.
B
Mary walked her bike across the avenue and up a short hill.
C
Mary rode her bike at a constant speed for one mile.
D
Mary used her bike to ride the first mile.
19

Which graph represents a function with a rate of change of 0 point 5 ?

A
Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points (negative 2 comma negative 2) and (4 comma 1).
B
Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points (negative 2 comma negative 5) and (2 comma 3).
C
Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points (negative 4 comma 1) and (2 comma negative 2).
D
Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points (negative 2 comma 3) and (1 comma negative 3).
20

On the way to the mall Miguel rides his skateboard to get to the bus stop. He then waits a few minutes for the bus to come, then rides the bus to the mall. He gets off the bus when it stops at the mall and walks across the parking lot to the closest entrance. Which graph correctly models his travel time and distance?

A
Image with description On a first quadrant graph, the horizontal axis is labeled time and the vertical axis is labeled speed. From left to right, the graph begins at the origin and moves to a point that is 2 ninths of the way across the horizontal axis and 1 ninth of the way up the vertical axis, moves to a point that is 3 ninths of the way across the horizontal axis and 3 ninths of the way up the vertical axis, moves to a point that is 4 ninths of the way across the horizontal axis and 3 ninths of the way up the vertical axis, moves to a point that is 5 ninths of the way across the horizontal axis and 5 ninths of the way up the vertical axis, and then ends at a point that is 8 ninths of the way across the horizontal axis.
B
Image with description On a first quadrant graph, the horizontal axis is labeled time and the vertical axis is labeled speed. From left to right, the graph begins at the origin and moves to a point that is 2 ninths of the way across the horizontal axis and 1 ninth of the way up the vertical axis, moves to a point that is 4 ninths of the way across the horizontal axis and 1 ninth of the way up the vertical axis, moves to a point that is 4 ninths of the way across the horizontal axis and 3 ninths of the way up the vertical axis, moves to a point that is 6 ninths of the way across the horizontal axis and 5 ninths of the way up the vertical axis, and then ends at a point that is 8 ninths of the way across the horizontal axis and 6 ninths of the way up the vertical axis.
C
Image with description On a first quadrant graph, the horizontal axis is labeled time and the vertical axis is labeled speed. From left to right, the graph begins at the origin and moves to a point that is 2 ninths of the way across the horizontal axis and 1 ninth of the way up the vertical axis, moves to a point that is 3 ninths of the way across the horizontal axis and 3 ninths of the way up the vertical axis, moves to a point that is 4 ninths of the way across the horizontal axis and 3 ninths of the way up the vertical axis, moves to a point that is 6 ninths of the way across the horizontal axis and 8 ninths of the way up the vertical axis, and then ends at a point that is 8 ninths of the way across the horizontal axis and 8 ninths of the way up the vertical axis.
D
Image with description On a first quadrant graph, the horizontal axis is labeled time and the vertical axis is labeled speed. From left to right, the graph begins at the origin and moves to a point that is 2 ninths of the way across the horizontal axis and 1 ninth of the way up the vertical axis, moves to a point that is 4 ninths of the way across the horizontal axis and 1 ninth of the way up the vertical axis, moves to a point that is 5 ninths of the way across the horizontal axis and 4 ninths of the way up the vertical axis, moves to a point that is 6 ninths of the way across the horizontal axis and 4 ninths of the way up the vertical axis, and then ends at a point that is 8 ninths of the way across the horizontal axis and 5 ninths of the way up the vertical axis.

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