Question

A painter is hired to paint the interior walls of a large warehouse. The function f(x)=20,000−40x models the area in square feet that remain to be painted, where x represents the number of minutes the painter has worked from the 100-minute mark through the 200-minute mark of the project.

What is the practical range of the function?

A) all integers

B) all real numbers between 100 and 200 inclusive

C) all real numbers between 12,000 and 16,000 inclusive

D) integers from 100 to 200 inclusive

Answer 1

Insert x = 100 and x = 200 in the function

f(100) = 20,000 - 40*100

= 20,000 - 4000

= 16,000

f(2)) = 20,000 - 8,000 = 12,000

So its choice C , All reals between 12,000 and 16,000 inclusive.

Answer 2

Option C.

Explanation:

The given function is

`f(x)=20000-40x`

where x represents the number of minutes the painter has worked from the 100-minute mark through the 200-minute mark of the project.

We need to find the practical range of the function.

The value of x lies from 100 to 200.

At x=100,

`f(100)=20000-40(100)=20000-4000=16000`

At x=200,

`f(200)=20000-40(200)=20000-8000=12000`

It means the practical range of the function is all real numbers between 12,000 and 16,000 inclusive.

Hence, the correct option is C.