contestada

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.

Respuesta :

Given:

The function is

[tex]f(x)=-5x-7[/tex]

To find:

The rate of change of the given function.

Solution:

We have,

[tex]f(x)=-5x-7[/tex]        ...(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

[tex]f(x)=mx+b[/tex]      ...(ii)

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

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

[tex]m=-5[/tex]

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.

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