Determine the degree of the following polynomial functions.
a. Suppose $f(x)=3 x^{6}+7 x^{2}+x-11$.
Degree of $f$ :
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b. Suppose $g(x)=9 x+3$.
Degree of $g$ :
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c. Suppose $h(x)=1+x+x^{2}+x^{3}$.
Degree of $h$ :
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Step 1 ：The degree of a polynomial is the highest power of the variable in the polynomial. So, to find the degree of a polynomial, we need to identify the term with the highest power of the variable and that power is the degree of the polynomial.

Step 2 ：For the polynomial function $f(x)=3 x^{6}+7 x^{2}+x-11$, the term with the highest power of the variable is $3 x^{6}$. Therefore, the degree of $f(x)$ is 6.

Step 3 ：For the polynomial function $g(x)=9 x+3$, the term with the highest power of the variable is $9 x$. Therefore, the degree of $g(x)$ is 1.

Step 4 ：For the polynomial function $h(x)=1+x+x^{2}+x^{3}$, the term with the highest power of the variable is $x^{3}$. Therefore, the degree of $h(x)$ is 3.

Step 5 ：Final Answer: The degree of $f(x)=3 x^{6}+7 x^{2}+x-11$ is \(\boxed{6}\). The degree of $g(x)=9 x+3$ is \(\boxed{1}\). The degree of $h(x)=1+x+x^{2}+x^{3}$ is \(\boxed{3}\).