May I have help with this?

Question

If f(x)= (x^2-4)/(x-2), then which of the following is true?

 

a.) x= 2 is a vertical asymptote

b.) can't be determined

c.) y=1 is a vertical asymptote

d) there are no vertical asymptotes

e.) x= -2 is a vertical asymptote

Answer 1

f(x)= (x^2-4)/(x-2) = (x+2)(x-2)/(x-2)

 

(x-2)/(x-2) is 1, except when x = 2 where it is undefined. This is a hole, not an asymptote.

 

So f(x) = x + 2, x ≠ 2 with no asyptotes.

Answer 2

Hi Mark;

f(x)= (x^2-4)/(x-2)

The denominator cannot equal zero.

0=x-2

2=x

The vertical asymptote is x=2.

a is correct.