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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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+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

 Apr 15, 2021
 #2
avatar+1436 
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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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+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
 #4
avatar+1436 
+2

Oh. I think I understand. Thank you both!

SmartMathMan  Apr 15, 2021

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