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What are the coordinates of the hole in the graph of the function f(x)=x2+4x−12/x−2

My answer is (-6,6)

I need help learning on how to do this though because I'm pretty sure im wrong

 Mar 8, 2019
 #1
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The x coordinate of the 'hole' in the graph occurs where the denominator = 0   

 

The numerator factors as   (x+6)(x-2)

 

so    (x+6)(x-2) / (x-2)     simplifies to   x +6  (realizing that the hole value of x cannot apply)   to find the 'y' value of the hole

 Mar 8, 2019
edited by Guest  Mar 8, 2019
 #2
avatar+111381 
+1

[ x^2 + 4x - 12 ] / [ x - 2] 

 

[ x+ 6 ] [ x - 2 ]  / [ x - 2 ]   =   x + 6    (1)  

 

The "hole"  occurs where the original denominator = 0

So

x - 2 = 0

x = 2  ⇒  the "hole"    (2)

 

To find the coordinates of the hole, put (2) into (1)

 

2 + 6  =  8

 

So....the "hole"  occurs at (2, 8)

 

 

 

cool cool cool

 Mar 8, 2019

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