Compare Characteristics of Two Functions

Madison created two functions. For Function A, the value of y is two less than four times the value of x. The table represents Function B. In comparing the rates of change, which statement about Function A and Function B is true?

• Function A and Function B have the same rate of change.

• Function A has a greater rate of change than Function B has.

• Function A and Function B both have negative rates of change.

• Function A has a negative rate of change and Function B has a positive rate of change.

The table represents a linear function. Which function has a greater slope and a greater y-intercept than the linear function represented in the table?

• y = 2x + 8.5

• y = 5x + 6.5

• y = 3x + 7.5

• y = 10x + 5.5

Function J is shown on the coordinate grid. If the y-intercept of Function R is 3/2 greater than the y-intercept of Function J, which equation could represent Function R ?

• y = -x + 4.5

• y = 0.5x + 3

• y= 3x + 0.5

• y = 4.5x - 1

Function P is a linear function with a y-intercept of 5. Function Q is defined by the equation y = -1/3x + 4. Which statement must be true about functions P and Q?

• Both functions have the same slope.

• Both functions have a negative slope.

• The functions will have the same input when y = 0.

• The functions will have different outputs when x = 0.

Functions W and Z are both linear functions x. Which statement comparing the functions is true?

• The slope of Function W is equal to the slope of Function Z.

• The slope of Function W is less than the slope of Function Z.

• The y-intercept of Function W is equal to the y-intercept of Function Z.

• The y-intercept of Function W is less than the y-intercept of Function Z.

Which function of x has the least value for the y-intercept?

• A

• B

• C

• D

Two photographers offer different pricing plans for their services. The graph models the prices Photographer A charges. The table shows the prices Photographer B charges. Each photographer charges a one-time equipment fee and an hourly rate. Which statement about the two pricing plans is true?

• Photographer A charges $15 per hour more than Photographer B

• Photographer B charges $15 per hour more than Photographer A

• Photographer A’s equipment fee is $25 less than Photographer B’s

• Photographer B’s equipment fee is $25 less than Photographer A’s

The table represents linear Function F. The equation y = 4x + 2 represents Function G. Which statement is true?

• The rate of change of Function G is less than the rate of change Function F because 2 < 3

• The rate of change of Function G is less than the rate of change Function F because 4 < 9

• The rate of change of Function G is greater than the rate of change Function F because 2 > 9/7

• The rate of change of Function G is greater than the rate of change Function F because 4 > 3

Linear functions M and P are shown in the picture. In comparing the rates of change, which statement about Function M and Function P is true?

• Their rates of change differ by 2.

• Their rates of change differ by 4.

• Function M has a greater rate of change than Function P.

• Function M and Function P have the same rate of change.