Question

Find any points of discontinuity for the rational function.

Answer 1

Just remember, rational functions are always continuous on their domain.

Answer 2

So if you're to find points of discontinuity, it had best not be in the domain of your function :)
For what values of x does your function NOT have a defined value?

Answer 3

See, for instance, if your function takes
x = -7, then your denominator becomes zero, which cannot yield a defined value.

There is another value for x which would make the denominator zero.

Answer 4

x = –9, x = –7??

Answer 5

Right...
As you can see, the denominator has a factor of (x + 9)
The entire denominator is (x + 9)(x + 7)
If x = -7, the denominator becomes (2)(0) = 0
Which means x cannot be -7.
If x = -9, the denominator becomes (0)(-2) = 0
Which means x cannot be -9.

Every other value of x is acceptable, hence the function is continuous on every other value of x.

Hence, it is discontinuous at x = -7 and x = -9

:)

Answer 6

Well, that's about it. NOTE
I said something about
"Every other value of x is acceptable, hence the function is continuous on every other value of x"

This is only true because this is a rational function, which can be shown to be continuous on its domain. Since all other values of x are acceptable, all other values of x are in its domain, and the function is therefore continuous on said values of x.

Got that? That was a mouthful XD
That's it for now...
---
Terence out