Q. 24 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 15–26, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell

why not.

$F\left(x\right)=\frac{x^2-5}{x^3}$

Step-by-Step Solution

Answer

$F$ is not a polynomial function. It is the ratio of two distinct polynomials and the polynomial in the denominator is of positive degree.

Step 1: Given information

$F\left(x\right)=\frac{x^2-5}{x^3}$

Step 2: Calculation

$F\left(x\right)=\frac{x^2-5}{x^3}$

$F$ is not a polynomial function. It is the ratio of two distinct polynomials and the polynomial in the denominator is of positive degree.