Topic 3: Use Functions to Model Relationships

Is the relation shown below a function? Use the graph to justify your answer.

• No, the relation is not a function because the input 2 is paired with two different outputs (0 and 2).

• Yes, the relation is a function because each input has only one output.

• No, the relation is not a function because the input 0 is paired with two different outputs (2 and 4).

• Yes, the relation is a function because the input 2 is paired with two different outputs.

Tags

CCSS.8.F.A.1

Consider the two functions below. Which one of these functions is linear? What is its equation? Enter any answers to two decimal places.
Function A
x: 3, 6, 9, 12, 15
y: 5, 10, 15, 20, 25
Function B
[Graph of a curve]
Which of the following is correct?

• Function A is linear. Its equation is y = 1.67x + 0.

• Function B is linear. Its equation is y = 2x + 1.

• Function A is linear. Its equation is y = 3x + 2.

• Function B is linear. Its equation is y = 1.67x + 0.

Tags

CCSS.8.F.A.3

Which function has a greater rate of change?

Function A has a rate of change of ​ (a)   and Function B has a rate of change of​ (b)   , so Function​ (c)   has a greater rate of change.

• -5
• -4.5
• B
• A

Select all the ways that describe the graph of the function in interval 2.

• The function is increasing.

• The slope is negative.

• The function is decreasing.

• The function is constant.

• The slope is positive.

Tags

CCSS.8.F.B.5

The graph of a function is a line that passes through the coordinates (2, 11) and (8, 14). Write an equation in the form y = mx + b for this function.

• y = 0.5x + 10

• y = 2x + 7

• y = -0.5x + 12

• y = x + 9

Tags

CCSS.8.F.B.4

Natasha rides her bicycle to school. She rides slowly uphill for 5 minutes. Then she speeds up and rides at a consistent speed on a flat road for 15 minutes. The last 2 minutes of her ride, Natasha rides back downhill until she arrives at school. Sketch a graph of the behavior of the bike ride over time.

Tags

CCSS.8.F.B.5

Emma says that Function A and Function B have the same initial value. Is Emma correct? Justify your response.

• Yes, both functions have the same initial value.

• No, Function A has a different initial value than Function B.

• No, Function B has a different initial value than Function A.

• No, neither function has an initial value.

Tags

CCSS.8.F.A.2

A bicycle shop rents bicycles by the hour. It charges an equipment fee with every rental. The graph shows the cost of renting a bicycle for different periods of time. Write a linear function in the form y = mx + b to represent the situation.

• y = 10x + 20

• y = 20x + 10

• y = 10x - 20

• y = 20x - 10

Tags

CCSS.8.F.B.4

Points are shown plotted on the coordinate plane.The points represent a relation, where x is the input and y is the output. Complete the sentence to explain whether or not this set of points represents a function.

It​ ​ (a)   because​ (b)   .

• does represent a function
• each input only has one output
• does not represent a function
• one input has two outputs

Tags

CCSS.8.F.A.1