Question

Which of the following polynomials has an even degree and a negative leading coefficient?

Polynomial going down from the left and passing through the point negative 6 comma 0 and going to a local minimum and then going up through the point negative 2 comma 0 to a local maximum and then going down through the point 3 comma 0 to a local minimum and then going up to the right through the point 5 comma 0
Polynomial going up from the left and passing through the point negative 6 comma 0 and going to a local maximum and then going down through the point negative 1 comma 0 to a local minimum and then up through the point 2 comma 0 to a local maximum and then down to the right through the point 4 comma 0
Polynomial going up from the left and passing through the point negative 6 comma 0 and going to a local maximum and then going down through the point negative 2 comma 0 and 0 comma negative 6 to a local minimum and then up to the right through the point 5 comma 0
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0

Answer 1

Using limits, the polynomial that has an even degree and a negative leading coefficient is:

Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.

What is a limit?

A limit is given by the value of function f(x) as x tends to a value.

In this problem, to find the polynomial, we have to find the limits as x goes to infinity, hence:

$\lim_{x \rightarrow -\infty} f(x) = [tex]\lim_{x \rightarrow -\infty} -a x^n$

Since n is even, we have that:

• $\lim_{x \rightarrow -\infty} -a (-\infty)^n = -a \times \infty = -\infty$

• $\lim_{x \rightarrow \infty} -a (\infty)^n = -a \times \infty = -\infty$

Since it goes down to the left and down to the right, hence the function is:

Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.

More can be learned about limits at https://brainly.com/question/26270080

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