Question

How do I find the left limit and right limit for this function?

Answer 1

what would the parent function of this be?

Answer 2

1/x ?

Answer 3

excellent.

and what would we do to get 1/x to look like the one you have?

Answer 4

Um, shift it to the right 2? Or is it 1/2?

Answer 5

right the first time. so what does the parent graph look like when it's been shifted to the right 2 units?

Answer 6

f(x) = 1/x... g(x) = f(x-2) = 1/(x-2) that's the shift.

Answer 7

I thought it would have a vertical asymptote of x=2 because it shifted to the right 2, but it's still x=0. Why?

Answer 8

no, you're right. the vertical asymptote is at 2 but it heads to 2 different places depending which side you approach 2 from.

Answer 9

Are the single sided limits not infinite limits???