Definition of Point Discontinuity
A function is said to have a point of discontinuity at x = a or the graph of the function has a hole at x = a, if the original function is undefined for x = a, whereas the related rational expression of the function in simplest form is defined for
x = a.
Examples of Point Discontinuity
- Consider a function .
This function is undefined for x = 2. But the simplified rational expression of this function, x + 3 which is obtained by canceling (x - 2) both in the numerator and the denominator is defined at x = 2. Thus we can say that the function f(x) has a point of discontinuity at x = 2.
Solved Example on Point Discontinuity
Which of the following would replace the blank so that the rational function will have a point discontinuity?
A. x - 11
B. 2x + 13
C. Either A or B
D. x + 1
Correct Answer: C
Step 1: The function will have a point discontinuity if the denominator contains either of the binomials (x - 11) or (2x + 13).
Related Terms for Point Discontinuity
- Rational Expression
Additional Links for Point Discontinuity