Question

How do you graph `y=-5/x` using asymptotes, intercepts, end behavior?

Answer 1

See answer below

Explanation:

Given: `y = -5/x`

This is called a rational function: `(N(x))/(D(x))`.

Find vertical asymptote(s):

When `D(x) = 0` we have vertical asymptotes:

vertical asymptote at `x = 0`

End conditions:
The negative coefficient means the graph is reflected about the `x`-axis. So instead of starting in above the `x`-axis, the function starts below the `x`-axis.

Find y-intercept by setting `x = 0:`

`y = -5/0 => y =`undefined. `" no "y`-intercept

Find x-intercepts by setting `y = 0: " "0 = -5/x`

Multiply both sides by `x: " "0 * x = -5, " "0 = -5` Not TRUE

This means there is no `x`-intercepts.

graph{-5/x [-10, 10, -10, 10]}