Graphing Utilities and Functions

This video tutorial explains how to graph an equation using a graphing utility. It covers two methods of graphing: by hand and using a graphing utility. The tutorial provides a detailed example of graphing the equation y = 1/30 * x * (x^4 - 10x^2 + 39), including creating a table of values and sketching the graph. It emphasizes the importance of adjusting the viewing window to accurately represent the graph.

What are the two methods mentioned for graphing a function?

• Using a graphing utility and drawing freehand

• Using a graphing utility and by hand

• Using a computer and drawing freehand

• Using a calculator and by hand

What is the first step when using a graphing utility to graph an equation?

• Enter the equation into the calculator

• Solve for x

• Plot the points

• Solve for y

In the example provided, what is the equation being graphed?

• y = x^2 + 10x + 39

• y = 1/30 * x^2 * (x^4 - 10x^2 + 39)

• y = 1/30 * x * (x^4 - 10x^2 + 39)

• y = x^3 - 10x + 39

What is the purpose of creating a table of values when graphing?

• To find the maximum and minimum points

• To determine the slope of the line

• To plot points and understand the graph's shape

• To calculate the derivative

Which values are typically included in a standard table of values?

• 0, 1, 2, 3

• -1, 0, 1

• -2, -1, 0, 1, 2

• -3, -2, -1, 0, 1, 2, 3

Why is it important to adjust the viewing window on a graphing utility?

• To change the color of the graph

• To adjust the scale of the axes

• To see the entire graph and accurately represent the data

• To zoom in on specific points

What should you do if you can't see the graph after hitting the graph button?

• Turn off the calculator

• Check the equation for errors

• Adjust the viewing window

• Re-enter the equation

What is the x minimum and maximum suggested for the viewing window in the example?

• -20 and 20

• -5 and 5

• -15 and 15

• -10 and 10

What is the y minimum and maximum suggested for the viewing window in the example?

• -5 and 5

• -10 and 10

• -15 and 15

• -20 and 20

What is the purpose of sketching the graph after using the graphing utility?

• To create a more detailed graph

• To verify the graphing utility's accuracy

• To compare with other graphing methods

• To practice drawing skills