(x+2)/(x-3) is already a rational function with a linear binomial in both the numerator and denominator...
The vertical asymptote occurs when the slope is undefined, in this case when you have division by zero, when x=3. So the vertical asymptote is about the vertical line x=3.
The horizontal asymptote occurs about the horizontal line about the line y=k which f(x) approaches, but does not equal as x approaches ±oo. Which in this case is relatively intuitive, but if you weren't sure, you could divide all terms by the highest power of x, in this case:
(x/x+2/x)/(x/x-3/x) as x approaches oo is
(1+0)/(1-0)=1, so the horizontal asymptote is about the horizontal line y=1
The y-intercept occurs when x=0 so:
f(0) is just 2/-3=-2/3, so the y-intercept is the point (0, -2/3)
