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Lesson: Evaluating Continuity and Discontinuity of a Function at a Point

In this lesson, we learn about three types of function discontinuity at a given point which are removable, jump, and infinite discontinuities.

Worksheet: Evaluating Continuity and Discontinuity of a Function at a Point • 18 Questions

Q1:

Given , what can be said of the continuity of at ?

AThe function is discontinuous at because
BThe function is discontinuous at because is undefined.
CThe function is continuous at .
DThe function is discontinuous at because does not exist.
EThe function is continuous on .

Q2:

Let What can be said of the continuity of at ?

AThe function is discontinuous at because .
BThe function is continuous at .
CThe function is discontinuous at because does not exist.
DThe function is discontinuous at because is undefined.

Q3:

Given , if possible or necessary, define so that is continuous at .

AThe function cannot be made continuous at because is undefined.
B makes continuous at .
CNo value of will make continuous because does not exist.
DThe function is already continuous at .

Q4:

Given , if possible or necessary, define so that is continuous at .

AThe function cannot be made continuous at because is undefined.
B makes continuous at .
CNo value of will make continuous because does not exist.
DThe function is already continuous at .

Q5:

Given , if possible or necessary, define so that is continuous at .

AThe function cannot be made continuous at because is undefined.
B makes continuous at .
CNo value of will make continuous because does not exist.
DThe function is already continuous at .

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