Question

In Problems 2, determine whether the function is a polynomial function, rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not.

$f\left(x\right)=\frac{3x^5}{2x+1}$

Short answer

The given function is not a polynomial function.

The given function is a rational function.

Step-by-step solution

Given information

The given function is$f\left(x\right)=\frac{3x^5}{2x+1}$.

Determine the type of the function 

The function $f\left(x\right)$ is a rational function because it is a fraction of two polynomial functions. The polynomial in the denominator must not be equal to zero.

Write the conclusion

The function $f\left(x\right)$ is not a polynomial function. It is a rational function.