Question

3. Which of the following power functions best describes the end behavior (also known as long-run behavior)
of the polynomial y=-3x* +5x² + 3x –1?
(1) y=x*
(3) y = 3x
(2) y=-3x
(4) y = 5x?

Answer 1

The end behavior of $y=-3x^4+5x^2+3x-1$ is the direction as the x values changes

The power function that best describes the end behavior of the polynomial is $y = -3x^4$

How to determine the end behavior of the function?

The function is given as:

$y=-3x^4+5x^2+3x-1$

The above function is a 4th degree polynomial with a negative leading coefficient.

This means that:

The long-run behavior of the polynomial function is that: As x approaches infinity, the function approaches negative infinity.

$\mathbf{i.e.\ as \ x \to \infty, \ f(x) \to -\infty}$

The function that would have the above end behavior is another 4th degree polynomial with a negative leading coefficient.

From the options, we have:

$y = -3x^4$

Hence, the power function that best describes the end behavior of the polynomial is $y = -3x^4$

Read more about end behaviors at:

https://brainly.com/question/11275875