Question

Find the vertical asymptotes, if any, of the graph of the rational function.

Answer 1

The function is a rational function.

Let's see the graph of it, below:

We can easily see the vertical asymptotes, but we will algebraically find them.

Vertical Asymptote is a VERTICAL line that a curve doesn't not touch/cross bt comes very close to it.

To find the vertical asymptote of a rational function, we set the denominator equals zero and find the corresponding values of x.

Thus,

$\begin{gathered} x(x+5)=0 \\ So, \\ x=0, \\ or \\ x+5=0,x=-5 \end{gathered}$

So, there are 2 vertical asymptotes,

x = 0

x = -5

the graph shown above confirms this fact