Megan Herman

2022-09-23

What are the asymptotes of $y=\frac{5}{x}$ and how do you graph the function?

Alec Reid

Beginner2022-09-24Added 9 answers

It is important to see that $\frac{5}{x}$ is equal to $\frac{5{x}^{0}}{{x}^{1}}$

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 x makes this function have the denominator of zero.

In this case, it is zero. Therefore, the horizontal asymptote is y=0.

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 x.

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

Since the numerator has the lower power than the denominator, we have x=0 as our vertical asymptote.

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 x makes this function have the denominator of zero.

In this case, it is zero. Therefore, the horizontal asymptote is y=0.

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 x.

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

Since the numerator has the lower power than the denominator, we have x=0 as our vertical asymptote.

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