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

1 Answer
SCooke
Sep 22, 2017

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.
enter image source here

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