Question

How do you graph and find the discontinuities of `y=2/(x+1)`?

Answer 1

The discontinuities of this graph are when x = -1 or y = 0.

Explanation:

A discontinuity is a "hole" or gap in the graph where one or both coordinates are undefined. One way for this to happen is if x is -1. If x is -1, then the denominator of the right side of this equation is 2/0, which is undefined.

The other way to get a discontinuity is to find a y-value for which there is no x-value. If we plug 0 in for y, then `2/(x+1)` must equal 0. We know that that can't happen, because it would require x to be infinitely large.

Here is the graph (you can see asymptotes at x = -1 and y = 0).
graph{2/(x+1) [-21.01, 18.99, -9.68, 10.32]}