Question

What are the possible degrees for the polynomial function?

Answer 1

Answer: Even degrees of 6 or greater

Step-by-step explanation:

Degree of a polynomial is the highest power of its term (monomial) having non-zero coefficients.

Also, the degree is even or odd shows the end behavior of the polynomial and the value of the degree shows the maximum number of roots.(x-intercepts)

When we see the given diagram, we found that the function has at least 6 roots,

Thus, it has degree of 6 or more than 6.

Now, the end behavior of the given graph is,

$f(x)\rightarrow -\infty$  as $x\rightarrow \infty$

$f(x)\rightarrow -\infty$  as $x\rightarrow -\infty$

Which is the end behavior of an even function,

⇒ Given polynomial has even degree.

⇒ Second option is correct.

Answer 2

Even degrees of six or greater