Question

A moving company’s moving rates can be represented by the function f(x) = 3x + 400, where x is the number of miles for the move.

Another moving company’s rates can be represented by the function g(x) = 5x + 200.

Which function represents the difference between the moving companies' rates, h(x) = f(x) – g(x)?

h(x) = 2x + 200
h(x) = –2x + 200
h(x) = 5x – 200
h(x) = 5x + 600

Answer 1

h(x) = –2x + 200 function represents the difference between the moving companies rates h(x) = f(x) – g(x)

Solution:

Given that,

For company A, monthly rates can be represented by function f(x) = 3x + 400, for x number of miles.

For company B, moving rates can be represented by function g(x) = 5x + 200, for x number of miles.

Need to identify which is the correct expression for difference between the company moving rate that is

h(x) = f(x) – g(x)

On substituting given value of f(x) and g(x) in (1) we get

h(x) = (3x + 400) – (5x + 200)

=> h(x) = 3x – 5x + 400 -200

=> h(x) = -2x +200

Hence second option that is h(x) = -2x +200 is correct representation of difference between moving companies rates.