f(x) = quantity x squared plus x minus two divided by quantity x squared minus three x minus four

graph

a coordinate axis scaled by one.

domain and range

x and y intercept(s)

horizontal asymptote(s)

vertical asymptote(s)

F(x) = (x^2 + x - 2) / (x^2 - 3x - 4)

Domain is all real numbers except the valus of x for which x^2 - 3x - 4 = 0
(x + 1)(x - 4) = 0
x = -1, x = 4
Domain is all real numbers except x = -1 and x = 4.  (-∞, -1) ∪ (-1, 4) ∪ (4, ∞)
Range is all real numbers

x-intercepts are the values of x for which x^2 + x - 2 = 0
(x - 1)(x + 2) = 0
x = 1, x = -2
x-intercepts are x = 1 and x = -2

y-intercept is y = 1/2

It has no Horizontal asymptotes

Vertical asymptotes are x = -1, x = 4