<h2>
Step-by-step explanation:</h2>
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