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Step 1.The polynomial function that we have is:
[tex]y=7x^6+10x-7[/tex]The leading term is
[tex]7x^6[/tex]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:
[tex]\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}[/tex]In this case, the leading coefficient is:
[tex]7[/tex]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
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