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** \(x=-3\)

SmartMathMan Apr 15, 2021

#1**+2 **

(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

Guest Apr 15, 2021

#3**+3 **

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

ElectricPavlov
Apr 15, 2021