Question

Identify the holes, vertical asymptotes, and horizontal asymptotes of the following.


`f (x) = (2)/(x-3)`

Answer 1

Horizontal asymptote: y = 0

Vertical asymptote: x = 3

Explanation:

The vertical asymptote in this graph would be when x = 3 because it would make the denominator 0, which would make the equation undefined.

There will not be any holes in the graph, because there won't be any point undefined in the function except for when x = 3, but that's a vertical asymptote.

Now, for the horizontal asymptote, we see what value y approaches as x approaches plus and minus infinity. Since x is in the denominator, y will approach 0 when it's plus or minus infinity.

Horizontal asymptote: y = 0

Vertical asymptote: x = 3