Find the discontinuities of f (x) = 2x^2 + 5x - 12 / x+4

Factor top

2x^2+5x-12 = (x+4) (2x-3)

we now have

f (x) = [ (x+4) (2x-3) ] / (x+4)

therefor, we factor out (x+4) to get

f (x) = 2x-3

a line

remember that (x+4) we factore dout

that means

x+4=0

x=-4

at x=-4, there is a hole

to find the y value, input into simplified funciton

y=2x-3

y=2 (-4) - 3

y=-8-3

y=-11

(-4,-11) is a hole

so the discontinuity is that there is a hole at (-4,-11)