Question

How do you graph `y=(2x+2)/(3x+1)` using asymptotes, intercepts, end behavior?

Answer 1

Calculate those critical points, and then the shape and location of the curve will be easier to see.

Explanation:

The intercept (on one side only) is at `x = -1`. The asymptote is at `x = -(1/3)`. The limit on each side at `x → oo` is 0.6667 (the expression becomes `(2x)/(3x)` or `2/3`).
The plot is symmetrical around both asymptotes (x = -1/3 and y = 0.666666666)
Ignore the interconnecting line in the plot. It is where the asymptote would go.