Question

What graph would represent this function

Answer 1

**As the options are missing, I will try to explain you how to find one**

Given function: f(x) =
`(4)/(x)`

If you plug in the value of x = 0, you will get:

f(x) =
`(4)/(0) = \infty`

If you approach from the right, the value of f(x) near x = 0 will be +
`\infty`, whereas if you approach from the left, the value of f(x) near x = 0 will be -
`\infty`. It means that at x=0, there will be a discontinuity (as shown in only graph attached with the question.) If there is no discontinuity at x=0, you can ignore that option.

Now, if there are multiple graphs having discontinuity at x = 0, you can do the following step:

Plug in the value of x = 4 in the given function.

f(x) =
`(4)/(4) = 1`

It means that at x = 4, the value of y = f(x) will be +1.

Now Plug in the value of x = -4 in the given function.

f(x) =
`(4)/(-4) = -1`

It means that at x = 4, the value of y = f(x) will be -1.

Nutshell: The graph having the discontinuity at x = 0, and the y values to be +1 and -1 for x = +4 and x = -4 respectively, will be the correct option.

The graph of f(x) =
`(4)/(x)` is attached with the answer.