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Point Discontinuity

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?

Choices:

A. x - 11

B. 2x + 13

C. Either A or B

D. x + 1

Solution:

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
• Function
• Graph