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
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
[ 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)
+68 
