Question

What are the possible degrees for the polynomial function?

degrees of 4 or greater
even degrees of 4 or greater
degrees of 5 or greater
odd degrees of 5 or greater

Answer 1

odd degrees of 5 or greater

Answer 2

Odd degrees of 5 or greater

Explanation:

By the given diagram,

The end behavior of the function is,

`f( x )\rightarrow -\infty \text{ , as }x\rightarrow -\infty`,

`f( x )\rightarrow +\infty\text{ , as }x\rightarrow +\infty`

Which is the end behavior of a function has odd degree and positive leading coefficient,

So, the function must have odd degree.

Now, Again by the given graph,

The function has five x-intercepts,

Therefore, The function has at least five solutions,

⇒ The degree of the function is 5 or more than 5,

Hence, the function has Odd degrees of 5 or greater

⇒ Last option is correct.