Question

Sandra has a rectangular sheet of plastic that is 50 inches long by 40 inches wide. She wants to cut out a square with side lengths of x inches from each corner of the plastic sheet. She will then fold the flaps to make an open-top box. The volume, y, in cubic inches, of this plastic box can be expressed as y=(50−2x)(40−2x)x=4x3−180x2 2,000x. Sandra graphs this function on a coordinate plane. Which of the following statements correctly describes the domain of the function? A The domain is the set of all real numbers 0 B The domain is the set of all real numbers 0 C The domain is the set of all integers 0 D The domain is the set of all integers 0

Answer 1

The domain of the function y = 4x³ − 180x² + 2000x is the set of all real numbers greater than 0

What is the domain of the polynomial?

We are given the expression showing the volume of the plastic box as:

y = (50 − 2x)(40 − 2x)x = 4x³ − 180x² + 2000x

Where:

x is the side length in inches

Now, the side length cannot be negative and as such we can say it can only be positive.

Thus, we can conclude that the domain of the function is a set of all real numbers greater than 0