Graphing Functions and Analyzing Graphs

This video tutorial demonstrates how to use an online graphing calculator to plot a function, adjust the viewing window, and analyze the graph to find local maxima and minima. It also covers determining the intervals where the function is increasing or decreasing by examining a table of values and adjusting the graph's window settings for optimal viewing.

What is the first step in using the online graphing calculator for graphing a function?

• Adjust the window settings

• Determine the local maxima

• Analyze the table of values

• Enter the equation into the calculator

What issue might you encounter after plotting the graph initially?

• The graph might not display any points

• The graph might be upside down

• The viewing window might not show high and low points

• The graph might be in black and white

Why is it helpful to analyze a table of values before adjusting the window?

• To know how to adjust the window for better visibility

• To change the function notation

• To find the exact coordinates of the origin

• To determine the color of the graph

What x-values are important to include when adjusting the window for better graph visibility?

• x-values from 0 to 2

• x-values from -10 to 10

• x-values from 4 to 6 and 8 to 10

• x-values from 10 to 12

What is the relative minimum point identified on the graph?

• (4, -500)

• (9, -475)

• (10, -489)

• (5, -539)

What is the relative maximum point identified on the graph?

• (9, -475)

• (10, -489)

• (4, -500)

• (5, -539)

In which interval is the function increasing?

• From 9 to infinity

• From 5 to 9

• From 0 to 4

• From negative infinity to 5

In which intervals is the function decreasing?

• From negative infinity to 5 and from 9 to infinity

• From 0 to 4

• From 4 to 6

• From 5 to 9

What does the function do at the relative extrema?

• It becomes undefined

• It remains constant

• It changes from increasing to decreasing or vice versa

• It changes color

How can the intervals of increase and decrease be expressed?

• Using fractions

• Using interval notation or inequalities

• Using color codes

• Using decimal points