Let f(x) = (3x^2 − 12) /(x^2 − 2x − 3)

. Sketch a complete graph of f. Include all vertical and horizontal

asymptotes, all holes, and all x- and y-intercepts.

Question

Let f(x) = (3x^2 − 12) /(x^2 − 2x − 3)

. Sketch a complete graph of f. Include all vertical and horizontal

asymptotes, all holes, and all x- and y-intercepts.

anonymous · Answer

http://www.wolframalpha.com/input/?i=plot+%283x%5E2+%E2%88%92+12%29+%2F%28x%5E2+%E2%88%92+2x+%E2%88%92+3%29

anonymous · Answer

@eliassaab lol i already punched it into my phones wold ram alpha app i just don't understand the other questions what exactly is a hole?

anonymous · Answer

A hoe should be a point where the function is not continuous

the_fizicx99 · Answer

0.0 that sounded wrong xD

anonymous · Answer

@tHe_FiZiCx99 lmfao ikr?

anonymous · Answer

Factor the denominator
$$
x^2-2 x-3=(x-3) (x+1)
$$
at x=3 and x =-1 the function  is not continuous and it has vertical asymptotes

the_fizicx99 · Answer

She didn't mean it that way though lol xD I'm sure it was a typo.

anonymous · Answer

Also
$$
\lim_{x\to \infty } \, \frac{3
   x^2-12}{x^2-2
   x-3}=3
$$
Hence y=3 is a horizontal asymptote