Question

Determine the end behavior of the graph of the polynomial function. y=7x^6+10x^5-7

Answer 1

Step 1.The polynomial function that we have is:

`y=7x^6+10x-7`

The leading term is

`7x^6`

which means the leading coefficient is 7, and the degree of the polynomial is 6.

Step 2. When the degree of a polynomial is an even number, as in this case 6 is even, there are two options for the end behavior:

`\begin{gathered} If\text{ the leading coefficient is a positive number: } \\ up/up \\ If\text{ the leading coefficient is a negative number} \\ down/down \end{gathered}`

In this case, the leading coefficient is:

`7`

which is a positive number. Therefore, the end behavior of the polynomial is:

Up and Up.

Step 3. A graph of the function confirms the end behavior:

To the left, it goes up, and to the right, it also goes up.

Answer: Up and Up