Question

Madison created two functions.

For Function A, the value of y is two less than four times the value of x.

The table below represents Function B.
-3,-9
-1,5
1,-1
3,3

In comparing the rates of change, which statement about Function A and Function B is true?

A.

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

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

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

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

Answer 1

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

Explanation:

Function A.

The value of y is two less than four times the value of x.

This statement can be expressed as

`y=4x-2`

This linear function is expressed as slope-intercept form. Where the slope is

`m=4`

Function B.

This function is represented by the given table.

If you observe, the domain is defined as -3, -1, 1, 3. The range is defined as -9, -5, -1, 3.

The domain values increase two units. Range values increase by 4. So, the ratio or slope of this function is

`m=(4)/(2)=2`

If we compare the ratio of change (or slopes) of both function, we would find that Function A as a doble ratio of change than Function B. In other words, Function A has a greater rate of change than Function B.

Therefore, the right answer is B.