Megan Herman
2022-09-23
Answered

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

You can still ask an expert for help

Alec Reid

Answered 2022-09-24
Author has **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.

asked 2021-02-25

True or False. The graph of a rational operate could encounter a horizontal straight line.

asked 2020-11-05

Identify each of the following functions as polynomial, rational, algebraic, or transcendental

asked 2022-09-04

Is x=−7 an inverse variation?

asked 2022-07-10

Are rational functions between affine algebraic sets continuous with respect to the Zariski topology on their domain of definition?

asked 2021-02-15

Is $-18/6$ irrational, rational, natural, or integer

asked 2022-02-18

Help with figuring out the end behavior of a Rational Function.

What is the end behavior of:

$f\left(x\right)=\frac{2{x}^{2}+2}{{x}^{2}+9}$

Any help would be good

What is the end behavior of:

Any help would be good

asked 2022-02-15

Is the section df associated to a rational function f on a curve X a global section of the canonical sheaf $\omega}_{X$ ? I know its zeroes are the ramification points, but does it have poles?