Question

Which function models the area of a rectangle with side lengths of 2x-4 units and x+1 units?

(A) f(x)=2x^(2)-4x+4
(B) f(x)=2x^(2)+8x-4
(C) f(x)=2x^(2)-8x+4
(D) f(x)=2x^(2)-2x-4

Answer 1

The function that models the area of the rectangle is f(x) = 2x^2 - 2x - 4

Step-by-step explanation:

The formula for the area of a rectangle is length times width. In this case, the length is 2x-4 units and the width is x+1 units. So the function that models the area of the rectangle is:

f(x) = (2x-4)(x+1)

To simplify, you can use the distributive property to expand the expression:

f(x) = 2x^2 + 2x - 4x - 4

Combining like terms, the function can be written as:

f(x) = 2x^2 - 2x - 4