How do you graph #y = 3/x #?

1 Answer
Parabola
Jan 18, 2018

The graph should look like this: graph{3/x [-10, 10, -5, 5]}

Explanation:

Let's use some asymptotes to guide us.

First, since the numerator is in the lower degree than the denominator, the horizontal asymptote is #y=0#

Second, since #x=0# makes the function undefined, the vertical asymptote is #x=0#

We can now plug in the #x# values of #-5,-4,-3,-2,-1,0,1,2,3,4,5# into our function and graph the result.

We connect the points.
Remember: the graph should curve so that as we get closer to #x=0#, we get really really close to the #y# axis, and as we keep going to the left/right, we get closer and closer to 0, but never reach it.

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