Question

How can I do this with the function (x+2)/x-3

Create a rational function with a linear binomial in both the numerator and denominator.
Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.
Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.

Answer 1

y= (x+2)/(x-3)
This function exists for x≠3 (value that render the denominator nil)
If x →3 , then y→ ∞, then:
Vertical Asymptote x=3

Horizontal asymptotes ↔ lim y = 1
x→∞
Horizontal asymptotes y =1

x-intercept: for y= 0, x = -2

y-intercept: for x= 0, y = -2/3