+1438 Determine which statement is accurate for the given function: \(f(x) = {x^2-9 \over x+3}\)
a) The graph will have a hole.
b) The graph will have a vertical asymptote.
c) The graph will have a horizontal asymptote.
d) The graph will have a slant asymptote.
I found a) and d) to be correct. I can find both in the equation but am I only supposed to look for one? I'm confused.
For slant asymptotes, I got \(y = x-3\)
For the Hole, I got \(x=-3\)
(x-3)(x+3) / (x+3) it will have a hole when the denominator = 0 at x = -3
it reduces to x-3 <==== a line with a hole at x = -3
+1438 So the answer is a) ? But it also has a slant asymptote, doesn't it?
+36916 I don't think so....since part of the numerator cancels with the denominator it is just a line with a hole...
if the numerator was something like x^2-8 it would have a slant (oblique) asymtope
