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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.

Verified Answer :

Answer:

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

Step-by-step 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

\(m=\frac{4}{2}=2\)

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.

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