Question

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

Answer 1

The graph should look like this: graph{2/(x-1)-2 [-10, 10, -5, 5]}

Explanation:

Let us find the horizontal asymptote.
Since the numerator variable is raised to the power of zero, and the denominator variable is raised to the power of one, the horizontal asymptote is `y=0` for the function `y=2/(x-1)`. Since we know that this is subtracted by two with no multiplication to it, the original asymptote is now shifted downward two units.

Therefore, the horizontal asymptote is `y=-2`.

To find the vertical asymptote, we see which value makes the denominator zero. We see that it is one.

Therefore, the vertical asymptote is `x=1`

Now, we graph these two lines in a graph with a dashed line.

*Image from desmos.com

Now, we plug in some x values to the function.(Let's go for `-3,-2,-1,0,1,2,3`)
Look at the graph to find out whether you are right or not!
graph{2/(x-1)-2 [-10, 10, -5, 5]}

We graph the points and see whether they go along nicely with our asymptotes. If they do, connect them. Remember that this one goes on forever.

If you think that these points do not go close enough to the asymptotoes, try more x values.