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Chapter 2: Problem 3

Determine which functions are polynomial functions. For those that are, identify the degree. $$g(x)=7 x^{5}-\pi x^{3}+\frac{1}{5} x$$

Short Answer

Expert verified
The given function \(g(x)=7 x^{5}-\pi x^{3}+\frac{1}{5} x\) is a polynomial function and its degree is 5.

Step by step solution

01

Identify Polynomial Function

Look at the function \(g(x)=7 x^{5}-\pi x^{3}+\frac{1}{5} x\). Every term in this function is in the form \(a_n x^n\), where \(a_n\) is a constant and \(n\) is a nonnegative integer, so this is a polynomial function.
02

Determine Degree of Polynomial Function

The degree of a polynomial is the highest power of \(x\). In this case, the highest power of \(x\) is 5 in the first term \(7x^5\). So, the degree of the polynomial is 5.

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