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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.

Sample Question Videos

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06:05

Worksheet • 24 Questions • 2 Videos

Q1:

Discuss the continuity of the function 𝑓 at π‘₯ = βˆ’ 2 , given

  • A The function is continuous at π‘₯ = βˆ’ 2 .
  • B The function is discontinuous at π‘₯ = βˆ’ 2 because l i m π‘₯ β†’ βˆ’ 2 𝑓 ( π‘₯ ) does not exist.
  • C The function is discontinuous at π‘₯ = βˆ’ 2 because 𝑓 ( βˆ’ 2 ) β‰  𝑓 ( π‘₯ ) l i m π‘₯ β†’ βˆ’ 2 .
  • D The function is discontinuous at π‘₯ = βˆ’ 2 because 𝑓 ( βˆ’ 2 ) is undefined.

Q2:

Discuss the continuity of the function 𝑓 at π‘₯ = 2 , given

  • A The function is continuous at π‘₯ = 2 .
  • B The function is discontinuous at π‘₯ = 2 because l i m π‘₯ β†’ 2 𝑓 ( π‘₯ ) does not exist.
  • C The function is discontinuous at π‘₯ = 2 because 𝑓 ( 2 ) β‰  𝑓 ( π‘₯ ) l i m π‘₯ β†’ 2 .
  • D The function is discontinuous at π‘₯ = 2 because 𝑓 ( 2 ) is undefined.

Q3:

Find the values of π‘Ž and 𝑏 that make the function 𝑓 continuous at π‘₯ = βˆ’ 1 and π‘₯ = βˆ’ 6 , given that

  • A π‘Ž = 1 2 5 , 𝑏 = 3 7 5
  • B π‘Ž = 1 2 5 , 𝑏 = βˆ’ 2 5 7 5
  • C π‘Ž = 3 7 5 , 𝑏 = 1 2 5
  • D π‘Ž = βˆ’ 6 1 7 , 𝑏 = βˆ’ 1 2 7
  • E π‘Ž = βˆ’ 1 2 7 , 𝑏 = βˆ’ 6 1 7
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