Question

Asymptote question..?

Answer 1

Identify the asymptotes, removable discontinuities, and intercepts for the graph of each function.

\[y = (x^2 + 4x - 5)/(x^2 + 8x + 15)\]

So far I have...
Vertical asymptote: x = -3, x = -5
Horizontal asymptote: 1
x-intercepts: (1, 0) and (-5, 0)
Y-intercept: (0, -1/3)
removable discontinuity: x = -5

Answer 2

How does it look? Can the removable discontinuity (-5) also be an x-intercept and a vertical asymptote?

Answer 3

It's one or the other :)
If the factor (x+5) in the denominator `cancels with something in the numerator`, then it's a removable discontinuity.

If it doesn't cancel, then it's an asymptotic discontinuity.

Answer 4

Okay so in this case, it's a removable discontinuity (because (x+5) is a factor of both the numerator and denominator) but it is not an asymptote OR an x-intercept?

Answer 5

Ummm yes you are correct.

It is a removable discontinuity at x=-5,
the function doesn't exist there, no y-value, (-5, DNE).

Sooooo x=-5 can't be an x-intercept because x=-5 is not in the domain of the function. The function doesn't exist there. Yaaaa I think that's right :D brain... thinking...

Answer 6

So ya,
remove x=-5 from the asymptote list, and from the intercept list.

Hmm looks like you were Abble to figure out the rest, yay good job :D

Answer 7

Lol. Thanks :)

Love the Abble puns aha.

Answer 8

XD