Define Continuous and Discontinuous Functions

The video tutorial covers the concepts of continuous and discontinuous functions, explaining how to identify them through graphing. It discusses different types of discontinuities, including holes, jumps, and asymptotes, and introduces the terms removable and non-removable discontinuities. The tutorial emphasizes understanding these concepts both graphically and algebraically.

What is a key characteristic of a continuous function?

• It has several jumps.

• It can be drawn without lifting the pencil.

• It is undefined at many points.

• It has multiple breaks.

Which of the following is NOT a type of discontinuity discussed?

• Asymptotes

• Jumps

• Curves

• Holes

What is a removable discontinuity?

• A discontinuity that involves a horizontal line.

• A discontinuity that cannot be removed.

• A discontinuity that involves a vertical asymptote.

• A discontinuity that can be eliminated by redefining the function at a point.

How is a jump discontinuity characterized?

• By a smooth curve.

• By a sudden change from one function to another.

• By a hole in the graph.

• By a vertical asymptote.

What is true about a vertical asymptote?

• The graph crosses the asymptote.

• The graph is defined at the asymptote.

• The graph approaches but never touches the asymptote.

• The asymptote is a horizontal line.