Question

How do you find the discontinuity of a rational function?

Answer 1

The discontinuities of a rational function can be found by setting its denominator equal to zero and solving it.

Let's look at a simple example. Let us find the discontinuities of `f(x)={x-1}/{x^2-x-6}`.
By setting the denominator equal to zero,
`x^2-x-6=0`
By factoring it out,
`(x+2)(x-3)=0`
So, we have `x=-2` and `x=3`.
Hence, `f` is discontinuous at `x=-2` and at `x=3`.

Would this get you going?