1. f(x) = [ x^2 + 4x - 12] / [ x - 2]
Factor the numerator
f (x) = [ (x + 6) ( x - 2)] / (x - 2) "cancel" the (x - 2) factors
f(x) = ( x + 6 )
The hole in the graph will occur at f(2) = 2 + 6 = 8 ⇒ ( 2, 8)
2. The graph at the top left is correct
3. Vertical asymptote x = 7
Horizontal asymptote y = 2