Question

What it means for a rational function to be improper ?

Short answer

A Rational function is improper when the degree of denominator function is less than or equal to degree of numerator function.

Step-by-step solution

Step 1. Defination

A Rational function $Q\left(x\right)$which is ratio of two polynomial function localid="1651835937616" $P\left(x\right)\mathrm{and}R\left(x\right)$ such that$Q\left(x\right)=\frac{P\left(x\right)}{R\left(x\right)}$where $R\left(x\right)\ne 0$ is called improper if the degree of polynomial function of denominator i.e.$R\left(x\right)$ is less than the or equal to degree of the polynomial function in numerator i.e.$P\left(x\right)$

Step 2. Example

Example of rational function which is improper is $Q\left(x\right)=\frac{4x^4+7}{3x-1}$

Where$P\left(x\right)=4x^4+7\mathrm{and}R\left(x\right)=3x-1$.