Academic Calculus - Lesson 1.6 Day 2

​Lesson 1.6 - Day 2 - Finding discontinuities of Piecewise Functions

​Pull out your note packet and complete the examples in your notes as you go through these slides.

Multiple Select

Discuss the continuity of the function.

Check all that apply.

• $$\lim_{x\rightarrow1}f\left(x\right)=1$$

• f(1) = 1

• The function is continuous.

• The function is discontinuous at 1 because the limit does not exist.

Multiple Select

Discuss the continuity of the function.

(More than one answer is possible)

• Continuous

• Discontinuous at

  x = 2, nonremovable

• The limit exists at x = 2

• The discontinuity is removable.

Multiple Select

Discuss the continuity of the function.

Check all that apply.

• $$\lim_{x\rightarrow-1}f\left(x\right)=-1$$

• f(-1) = -1

• The function is continuous.

• The function is discontinuous at -1 because the limit does not exist.

Multiple Select

Discuss the continuity of the function.

Check all that apply.

• $$\lim_{x\rightarrow0}f\left(x\right)=1$$

• f(0) = -1

• The function is continuous.

• The function is discontinuous at 0 because the limit does not exist.

Multiple Choice

Discuss the continuity of the function shown.

• Discontinuous at x = 1, removable

• Discontinuous at x = 1, nonremovable

• Continuous

Multiple Choice

Discuss the continuity of the function shown.

• Discontinuous at x = -1, removable

• Discontinuous at x = -1, nonremovable

• Continuous

Multiple Choice

Discuss the continuity of the function shown.

• Discontinuous at x = 1, removable

• Discontinuous at x = 1, nonremovable

• Continuous