View Question - How To Find The Hole?

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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

Love2Read Mar 8, 2019
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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

Guest Mar 8, 2019edited by Guest  Mar 8, 2019 #2avatar+130561 +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

CPhill Mar 8, 2019 Post New Answer

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