Sketch the graph of f(x) = (2x-5)/(x^2-x-6) ?

Question

I have this question here.

Sketch the graph of f(x) = (2x-5)/(x62-x-6).

I have simplified the equation to (2x-5)/ [(x+2)(x-3)]

Seems like there's a point at -2 and 3,

How do I get the points to sketch the graph?

Answer 1

you have vertical asymptotes at x = -2& 3 and a horizontal at y = 0....from left to right: starts just below the x axis and as it screams down as you approach x = -2, then starts again way high and drops rapidly passing through (5/2,0) and again screams down as you approach x = 3, way high on the other side and drops down to the x axis for huge x..."two wings separated by an elongated S " if you have had derivatives then you could compute f ' ' , set to 0 and find the inflection point on the "S" portion of the graph