How do you determine the value of #A# such that #f(x)# has a point discontinuity without using trial and error?
A point of discontinuity is also known as a hole. For example, the graph of
The trick about holes is that they occur when a common factor is cancelled out in the numerator and the denominator.
Start by factoring the expression that we know: the denominator.
Now let's compare this to the numerator. There is no way that we can make
Let's do a final check.
So, there will be a discontinuity at
Hopefully you understand now!