Question

PLEASE HELP

Which statement about the function y = –2x3 is correct?
A. The function is nonlinear and could be made linear by changing -2 to 2.
B. The function is nonlinear and could be made linear by changing 3 to 1.
C. The function is linear and could be made nonlinear by changing -2 to 2.
D. The function is linear and could be made nonlinear by changing 3 to 1.

Answer 1

B.

Explanation:

So we have the function:

`y=-2x^3`

As we can see, the degree of this function is 3. This is a cubic function. In other words, this is nonlinear. Let's go through each of the choices:

Already, we can eliminate C and D since the function is nonlinear as it's a cubic function. So, we only need to check A and B.

A: If we change the -2 to 2 like so:

`y=-2x^3\\y=2x^3`

The function remains a cubic. The only thing we've changed is how the graph is oriented. With -2, the graph goes from top to bottom. With 2, the graph goes from bottom to top. Nevertheless, it's still a cubic function. What we need to change is the exponent and not the coefficient. A is not correct.

B: If we change the 3 to 1 like so:

`y=-2x^3\\y=-2x^1\\y=-2x`

This is now a linear equation. The degree is 1 and as you can probably picture, it's a downwards sloping line. The correct answer is B.