Question

#22Graph the function and tell wether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell wether it is removable or non removable.

Answer 1

Answer:

Removable discontinuity at x=0.

Step-by-step explanation:

By looking at the denominator of h(x), there will be a discontinuity.

Since the denominator cannot be zero, x has to be different from 0. Therefore, there is a discontinuity at x=0.

Now, to determine what type of discontinuity, check if there is a common factor in the numerator and denominator of the function. If there is an existent common factor, there is a removable discontinuity or a hole.

$\begin{gathered} h(x)=\frac{x^3+x}{x} \\ h(x)=\frac{x(x^2+1)}{x}=x^2+1 \end{gathered}$

There is a removable discontinuity, or a hole, at x=0.