Question

how do i find the vertical asymptote?

Answer 1

do u have a rational function ?

Answer 2

yea its f(x)=x-2/x^2-5x+6

Answer 3

a vertical asymptote or a hole occurs when denominator approaches 0

Answer 4

start by factoring he denominator

Answer 5

x^2-5x+6

could u factor this

Answer 6

(x-3)(x-2)

Answer 7

so we have a common factor !

Answer 8

\( f(x) = \frac{x-2}{(x-2)(x-3)} \)

Answer 9

\((x-2) \) cancels top and bottom, right ?

Answer 10

yes

Answer 11

and denominator becomes 0, when x = 2, or x = 3

Answer 12

but since (x-2) is getting cancelled, it is just a hole. its not a vertical asymptote
since (x-3) is not getting cancelled, it is a proper vertical asymptote

Answer 13

x-3 = 0
x = 3

we say the line x = 3 is the vertical asymptote of rational function

Answer 14

thanks i understand now

Answer 15

glad to hear :)