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# Algebra 2 Help Needed!

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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  $$x=-3$$

Apr 15, 2021

#1
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(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

Apr 15, 2021
#2
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So the answer is a) ? But it also has a slant asymptote, doesn't it?

SmartMathMan  Apr 15, 2021
#3
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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
#4
+1436
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Oh. I think I understand. Thank you both!

SmartMathMan  Apr 15, 2021