Question

How do I find the hole(s) in the Rational Function
f(x)=(x-2) / ((x^2)+2x-15) ?

Answer 1

see if denominator has a factor of (x-2)

Answer 2

if so, it would cancel the numerator and creates a hole at x=2

Answer 3

so if it doesn't cancel then there isn't one?

Answer 4

thats right, if it doesnt cancel no holes

Answer 5

we will have all vertical asymptotes

Answer 6

holes occur only when some factor cancels in the denominator,
it removes the vertical asymptote and creates a hole

Answer 7

how do I find a verticle asymptote?

Answer 8

equate the denominator to 0

Answer 9

find the solutions by factoring it

Answer 10

((x^2)+2x-15) = 0

Answer 11

there can be 2 vertical asymptotes here if nothing cancels the numerator
else, 1 vertical asymptote and 1 hole are possible

Answer 12

((x^2)+2x-15) = 0

(x-3)(x+5)=0
x =3, x = -5

two VAs !

Answer 13

how do I graph them?

Answer 14

we show VAs in graph with dotted lines