Question

Which statement describes the rate of change of the following function?

f(x) = -5x - 7

A.
The function has a varying rate of change when x < 7.
B.
The function has a varying rate of change when x < 5.
C.
The function has a constant rate of change, decreasing for all x at a rate of 7.
D.
The function has a constant rate of change, decreasing for all x at a rate of 5.

Answer 1

Given:

The function is

`f(x)=-5x-7`

To find:

The rate of change of the given function.

Solution:

We have,

`f(x)=-5x-7` ...(i)

It is a linear function because the degree or power of x in this function is 1.

Slope of a linear function is always constant.

The slope intercept form of a linear function is

`f(x)=mx+b` ...(ii)

where, m is slope and b is y-intercept.

On comparing (i) and (ii), we get

`m=-5`

It means, the function has a constant rate of change, decreasing for all x at a rate of 5.

Therefore, the correct option is D.