Understanding Graphs and Extrema

This video tutorial demonstrates how to graph functions using Desmos and analyze the graphs to determine intervals where the function is increasing or decreasing. It also covers identifying relative extrema, such as relative minimums and maximums, and provides examples to illustrate these concepts. The tutorial guides viewers through using Desmos to input functions, adjust graph views, and interpret key points on the graph.

What tool is used in the video to graph functions?

• GraphCalc

• Wolfram Alpha

• Desmos

• GeoGebra

How do you determine if a function is increasing on a graph?

• The graph moves downhill from left to right.

• The graph moves uphill from left to right.

• The graph is horizontal.

• The graph forms a loop.

What is the interval notation for a function increasing from negative infinity to -2?

• (-2, ∞)

• (-∞, -2)

• (-∞, 0)

• [0, -2]

What is a relative minimum?

• A point where the function changes from increasing to decreasing.

• A point where the function changes from decreasing to increasing.

• The highest point on the graph.

• A point where the graph is horizontal.

How is a relative maximum represented?

• As a single number.

• As a graph line.

• As a function equation.

• As an ordered pair.

In the first example, what is the relative maximum value?

• 2

• -2

• 3

• -3

What is the x-value where the function changes from increasing to decreasing in the first example?

• 2

• -3

• 3

• -2

In the second example, what is the relative minimum value?

• -3

• 3

• 2

• -2

What is the x-value where the function changes from decreasing to increasing in the second example?

• 2

• 3

• -3

• -2

What is the interval notation for a function decreasing from negative infinity to 2?

• [0, 2]

• (-∞, 0)

• (2, ∞)

• (-∞, 2)