$$ 1 \leftarrow $$ Determine whether the function is a polynomial function. If it is, identify the degree. $$ g(x)=2 x^{7}-\pi x^{4}+\frac{1}{7} x^{3} $$ Choose the correct choice below and, if necessary, fill in the answer box to complete your choice. A. It is a polynomial. The degree of the polynomial is B. It is not a polynomial.

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1. The given function is  
   $$
   g(x)=2x^7-\pi x^4+\frac{1}{7}x^3.
   $$
2. A polynomial is an expression consisting of terms of the form $$ ax^n $$ where $$ a $$ is a constant and $$ n $$ is a nonnegative integer.
3. In $$ g(x) $$, the powers of $$ x $$ are $$ 7 $$, $$ 4 $$, and $$ 3 $$, each of which is a nonnegative integer.
4. Thus, $$ g(x) $$ is indeed a polynomial function.
5. The degree of a polynomial is the largest exponent of $$ x $$ that appears in the function. Here, the largest exponent is $$ 7 $$.

Answer: A. It is a polynomial. The degree of the polynomial is $$ 7 $$.
It is a polynomial, and its degree is 7.

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