Question

Which function has the following characteristics?

A vertical asymptote at x = 3
A horizontal asymptote at y = -1/2

Answer 1

Looks like the (1/x) or (-1/x) graphs.

To get the vertical asymptote, have the denominator such that when you equate the denominator to 0, x=3. i.e. x=3 ==> x-3 = 0.

To get the horizontal asymptote, you'd have to shift the graph such that the new "y-axis" is -1/2. To do this, substitute y with y-1/2.

1) For 1/x:
y-1/2 = 1 / (x-3)

2) For (-1/x):
y-1/2 = -1 / (x-3)

Answer 2

What? Im kinda confused.