Question

The graph below shows the function f (x) = StartFraction x minus 3 Over x squared minus 2 x minus 3 EndFraction.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A hole is at x = 3. Both curves approach x = negative 1.

Which statement is true?
There is a hole at x = 3 and an asymptote at x = –1.
There is an asymptote at x = –1 and no hole.
There is a hole at x = 3 and no asymptote.
There is an asymptote at x = 3 and a hole at x = –1.

Answer 1

There is a hole at x = 3 and an asymptote at x = –1.

Explanation:

I got it on edge

Answer 2

There is a hole at x = 3 and an asymptote at x = –1.

Explanation:

f(x) = (x-3)/(x²-2x-3)

f(x) = (x-3)/(x-3)(x+1) = 1 / x+1 (x=3 is a hole)

asymptote while x+1 --> 0 and f(x) -->∞

x = -1 is vertical asymptote