Question

Describe the vertical asymptote(s) and hole(s) for the graph of y = (x+2)(x+4)/(x+4)(x+1)

Answer 1

does anything cancel in (x+2)(x+4)/(x+4)(x+1)

Answer 2

1?

Answer 3

notice you have a pair of "x+4" terms

Answer 4

so they would cancel

Answer 5

Ok so the hole is 4?

Answer 6

close, the hole is actually -4, this is because (x+2)(x+4)/(x+4)(x+1) simplifies to (x+2)/(x+1)

it has a vertical asymptote at x = -1 because this makes the denominator x+1 equal to zero

but to make (x+2)(x+4)/(x+4)(x+1) equivalent to (x+2)/(x+1), you have to add the further restriction that x can't equal -4, which causes the hole there

Answer 7

so the asymptote is -1? this is much clearer lol thank you!!1

Answer 8

yes it is, yw