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Lesson: Determining the Continuity or Discontinuity of a Function at a Point

In this lesson, we will learn how to differentiate between the three types of function discontinuity at a given point.

Question Video: Discussing the Continuity of a Piecewise Defined Function at a Point

11:03

Worksheet: Determining the Continuity or Discontinuity of a Function at a Point • 19 Questions

Q1:

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

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

Q2:

Let What can be said of the continuity of at ?

  • A The function is continuous at .
  • B The function is discontinuous at because is undefined.
  • C The function is discontinuous at because .
  • D The function is discontinuous at because does not exist.

Q3:

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

  • A makes continuous at .
  • BThe function is already continuous at .
  • CThe function cannot be made continuous at because is undefined.
  • DNo value of will make continuous because does not exist.

Q4:

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

  • A makes continuous at .
  • BThe function is already continuous at .
  • CThe function cannot be made continuous at because is undefined.
  • DNo value of will make continuous because does not exist.

Q5:

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

  • A makes continuous at .
  • BThe function is already continuous at .
  • CThe function cannot be made continuous at because is undefined.
  • DNo value of will make continuous because does not exist.

Q6:

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

  • A makes continuous at .
  • BThe function is already continuous at .
  • CThe function cannot be made continuous at because is undefined.
  • DNo value of will make continuous because does not exist.

Q7:

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

  • A makes continuous at .
  • BThe function is already continuous at .
  • CThe function cannot be made continuous at because is undefined.
  • DNo value of will make continuous because does not exist.

Q8:

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

  • AThe function cannot be made continuous at because does not exist.
  • BThe function is already continuous at .
  • C would make continuous at .
  • D would make continuous at .

Q9:

Discuss the continuity of the function at , given

  • A The function is continuous at .
  • B The function is discontinuous at because does not exist.
  • C The function is discontinuous at because .
  • D The function is discontinuous at because is undefined.

Q10:

Suppose What can be said of the continuity of at ?

  • A The function is continuous at .
  • B The function is discontinuous at because .
  • C The function is continuous on .
  • D The function is discontinuous at because is undefined.
  • E The function is discontinuous at because does not exist.

Q11:

Discuss the continuity of the function at given

  • A The function is discontinuous at because does not exist.
  • B The function is discontinuous at because .
  • C The function is discontinuous at because is undefined.
  • D The function is continuous at .

Q12:

Find the value of that makes continuous at , given that

Q13:

Find the value of that makes continuous at , given that

Q14:

Find the value of that makes continuous at , given that

Q15:

Setting and when makes continuous at . Determine .

  • A3
  • B
  • C
  • D2

Q16:

Setting and when makes continuous at . Determine .

  • A2
  • B
  • C
  • D

Q17:

Find the values of and that make the function continuous at and , given that

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q18:

Consider the function

What is ?

What is ?

What is ?

What type of discontinuity does the function have at ?

  • AThe function has a removable discontinuity at .
  • BThe function does not have a discontinuity at .
  • CThe function has an essential discontinuity at .
  • DThe function has a jump discontinuity at .

Q19:

Consider the function

What is ?

What is ?

  • AThe limit does not exist.
  • B1
  • C0
  • D
  • E

What is ?

  • A
  • B1
  • C0
  • D
  • EThe limit does not exist.

What type of discontinuity does the function have at