Question

You are calculating the volume of a box which has a width ofx inches, a

Answer 1

Using limits, it is found that the end behavior of the polynomial function for the volume of the rectangular box is:

B. down and up.

What is the volume of a rectangular prism?

The volume of a rectangular prism of length l, width w and heigth h is given by:

V = lwh.

In this problem, we have that the dimensions are given by:

• w = x.

• l = x - 1.

• h = x - 2.

Hence the volume is given by:

$V = x(x - 1)(x - 2) = x(x^2 - 3x + 2) = x^3 - 3x^2 + 2x$

What is the end behavior of a function?

It is given by it's limits as x goes to infinity.

Hence:

$\lim_{x \rightarrow -\infty} V(x) = \lim_{x \rightarrow -\infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow -\infty} x^3 = -\infty$

$\lim_{x \rightarrow \infty} V(x) = \lim_{x \rightarrow \infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow \infty} x^3 = \infty$

Which means that option B is correct.

More can be learned about limits at brainly.com/question/22026723