# What are the asymptotes of #y=5/x# and how do you graph the function?

##### 1 Answer

The graph should look like this: graph{5/x [-10, 10, -5, 5]} with the asymptotes of

#### Explanation:

It is important to see that

As for graphing this, try to graph -3,-2,-1,0,1,2,3 as the x values. Plug them in to get the y values. (If any of them give you an undefined answer, skip that one.)

See if these values show quite clearly of what the asymptotes are.

Since our case may not seem so clear, we graph larger values. Remember to connect the points to get the graph.

(You can try -10,-5,0,5,10)

To find the horizontal asymptote, we try to find which value for

In this case, it is zero. Therefore, the horizontal asymptote is

To find the vertical asymptote, there are three situations to look at:

-Does the numerator have higher power than the denominator?

-Does the numerator have the same power as the denominator?

-Does the numerator have the lower power than the denominator?

For the first case, we divide the numerator and the denominator to get the asymptote.

For the second case, we divide the coefficients of

For the third case, we simply say that it is zero.

Since the numerator has the lower power than the denominator, we have