Chapter 4, Problem 1RE

In Problems $1-4$, determine whether the function is a polynomial function, a rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not.

$f\left(x\right)=4x^5-3x^2+5x-2$

To determine

Whether the function $f(x)=4x^5-3x^2+5x-2$ is a polynomial function, a rational function, or neither. If polynomial, state degree, otherwise tell why not.

Answer to Problem 1RE

Solution:

Function $f(x)=4x^5-3x^2+5x-2$ is a polynomial function of degree 5

Explanation of Solution

Given Information:

The function, $f(x)=4x^5-3x^2+5x-2$

The polynomial function is in standard form of $f(x)=a_n{x}^n+a_{n-1}{x}^{n-1}+\mathrm{....}+a_{1}x+a_0$.

Hence, $f(x)=4x^5-3x^2+5x-2$ is a polynomial function.

It has leading term $4x^5$.

Hence, function $f(x)=4x^5-3x^2+5x-2$ is a polynomial function of degree 5.