Question

60 POINTS!!! HELPFind any asymptotes or holes in the function below. Explain how you arrived at your answer. SHOW YOUR WORK AND THE STEPS YOU TOOK.

Answer 1

The function given is,

$y=\frac{x-6}{(x-1)(x-6)}$

Since , the leading coefficient of numerator is less than the leading coefficient of denominator .

Therefore, there is no horizontal asymptotes.

For finding the vertical asymptotes, substitute the denominator is equal to 0.

$(x-1)=0\text{ , }(x-6)=0$$x=\text{ 1,6.}$

The vertical asymptotes are 1 and 6.

To find the hole in the function,

$(x-6)$

is crossed out in numerator and denominator.

So, if we set up x-6 equals to 0.

The hole in the function is, when

$x=6.$