State any x and y intercepts as well as any holes and asympt

State any x and y intercepts as well as any holes and asymptotes x-4 f(x) = x2-x-6 CX- X-3) x+2)

Ans: y intercept when x = 0, so y intercept = (0-4)/(0-3)*(0+2) = -3/2.

x intercept when y = 0 i.e, numerator is zero in the domain. Here x = 4 is the x intercept.

Vertical asymptotes occur when denominator is zero. So, (x-3)*(x+2) = 0. x = -2, 3 are the vertical asymptotes.

Since the degree of numerator is (1) less than denominator (2) so it\'ll have a horizontal asymptote at y = 0 i.e. x axis.

This will have no slant asymptotes.