Determine all numbers at which the function is continuous.

If the graph of any function is an unbroken curve, then the function is continuous. Let's study the function at the the point [/tex]x=5[/tex]:

At this point the function has the following value:

, so the function in fact exists here, but let's find the limit here using:

So:

By factoring out this function we have:

Since then the function is continuous here.

Let's come back to our function:

If we factor out this function we get:

Notice that at x = 9 the denominator becomes 0 implying that at this x-value there is a vertical asymptote. The graph of this function is shown below and you can see that at x = 9 the function is not continous

Therefore, the answer is:

b. continous at every point exept

step-by-step explanation:

see if this :