Question

Consider the leading term of the polynomial function. What is the end behavior of the graph?
2x^7 – 8x^6 – 3x^5 – 3

A. The leading term is 2x^7. Since n is odd and a is positive, the end behavior is up and up.

B. The leading term is 2x^7. Since n is odd and a is positive, the end behavior is down and down.

C. The leading term is 2x^7. Since n is odd and a is positive, the end behavior is down and up.

D. The leading term is 2x^7. Since n is odd and a is positive, the end behavior is up and down.

Answer 1

Answer:

Option C.

Step-by-step explanation:

A polynomial is defined as

$P(x)=ax^n+bx^{n-1}+...+c$

where, $ax^n$ is leading term.

If n is even and a is positive, then the end behavior is up and up.

If n is even and a is negative, then the end behavior is down and down.

If n is odd and a is positive, then the end behavior is down and up.

If n is odd and a is negative, then the end behavior is up and down.

The given polynomial is  

$P(x)=2x^7-8x^6-3x^5-3$

In this polynomial leading term is $2x^7$.

a=2 and n=7, which is odd.

Since n is odd and a is positive, therefore the end behavior is down and up.

Answer 2

We want to analyze the end behavior of a graph of a given polynomial by the degree and leading coefficient.

The correct option is C: "The leading term is 2x^7. Since n is odd and a is positive, the end behavior is down and up."

The general rule to know this is:

If the degree is even, then the two arms of the polynomial go in the same direction, then if the leading coefficient is positive, both ends go up.

If the leading coefficient is negative, both ends go down.

In the case where the degree is odd, each end go in a different direction.

If the leading coefficient is positive, the first end (the one for the negative values) go down, and the other end goes up.

When the leading coefficient is negative the inverse happens.

Here we have the polynomial:

p(x) = 2*x^7 - 8*x^6 - 3*x^5 - 3

We can see that the degree is 7, so it is odd, and the leading coefficient is positive (is equal to 2).

Then the first end goes down and the second goes up, thus the correct option is C.

If you want to learn more, you can read:

https://brainly.com/question/11536910