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

Solution:

Given, y = 5/x

We have to find the asymptotes of y = 5/x.

Consider the rational function R(x) = axⁿ/bx^m

Where n is the degree of the numerator

m is the degree of the denominator

1) If n < m, then the x-axis, y = 0, is the horizontal asymptote.

2) If n = m, then the horizontal asymptote is the line y = a/b

3) If n > m, then there is no horizontal asymptote (there is an oblique asymptote)

Now, y = 5/x = 5x⁰/x¹

Here, n = 0 and m = 1.

So, n < m ie., 0 < 1

So, the x-axis, y = 0, is the horizontal asymptote.

Therefore, vertical asymptote x = 0

Horizontal asymptote y = 0

No oblique asymptote.

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

Summary:

The asymptotes of y = 5/x are vertical asymptote x = 0, horizontal asymptote y = 0, no oblique asymptote.