Removable discontinuities from a graph

The video tutorial explains how to determine if a function is continuous by using the pencil test on a graph. It introduces the concept of discontinuities, distinguishing between removable and non-removable types. Removable discontinuities are identified by holes in the graph, while non-removable ones include jump discontinuities and vertical asymptotes. The tutorial emphasizes using X values to locate discontinuities within the domain.

What is a simple way to determine if a function is continuous?

• By counting the number of peaks in the graph

• By measuring the length of the graph

• By checking if the graph can be drawn without lifting the pencil

• By calculating the area under the graph

What type of discontinuity is characterized by a hole in the graph?

• Jump discontinuity

• Removable discontinuity

• Vertical asymptote

• Horizontal asymptote

Which values are used to identify the location of a discontinuity in a function?

• Y values

• Z values

• X values

• W values

What is a jump discontinuity?

• A point where the graph is tangent to the Y-axis

• A transition from one function to another

• A point where the graph has a hole

• A point where the graph crosses the X-axis

Which type of asymptote is considered a discontinuity of the graph?

• Curved asymptote

• Diagonal asymptote

• Horizontal asymptote

• Vertical asymptote