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Chapter 2: Problem 2

Determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=7 x^{2}+9 x^{4}$$

Short Answer

Expert verified
Yes, the function \(f(x) = 7 x^2 + 9 x^4\) is a polynomial function and its degree is 4.

Step by step solution

01

Understand Polynomial Functions

A polynomial function has the form \(P(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_2 x^2 + a_1 x + a_0\), where \(n\) is a whole number and \(a_0 , a_1 , ..., a_n\) are coefficients. The function is continuous and smooth when graphed. The degree of the polynomial is the highest power of \(x\) in the polynomial function.
02

Identify Polynomial Function

Now, consider the function \(f(x) = 7 x^2 + 9 x^4\). It is clear that this function adheres to the form of a polynomial function as there are no negative powers, fractional powers or other strange terms that violate the rules of a polynomial function.
03

Identify the Degree

The degree of the polynomial is the highest power of \(x\) in the polynomial. Here, the highest power of \(x\) in our function is 4. Therefore, the degree of the polynomial \(f(x) = 7 x^2 + 9 x^4\) is 4.

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