Graphing Piecewise Functions with a Calculator

The video tutorial explains how to graph piecewise functions using tables. It begins with an introduction to piecewise functions, describing them as functions with multiple rules based on input values. The tutorial then demonstrates how to graph these functions using tables, providing three examples with varying numbers of rules. The instructor uses color coding and calculators to plot points and emphasizes the importance of understanding domain boundaries. The video concludes with a call for practice in class.

What is a piecewise function?

• A function with multiple rules based on input values

• A function that only uses linear equations

• A function with a single rule for all input values

• A function that cannot be graphed

In a piecewise function, what do the curly brackets represent?

• The rules and domains of the function

• The x and y intercepts

• The range of the function

• The slope of the function

When graphing the first example, what color was used for the first piece?

• Blue

• Green

• Yellow

• Red

For the first example, what is the rule for numbers less than or equal to -3?

• x - 4

• 2x - 5

• x + 4

• -2x - 5

In the first example, what type of circle is used at the point (-3, 1) for the first rule?

• Open circle

• Closed circle

• Dashed circle

• No circle

In the second example, what is the rule for numbers smaller than -2?

• 1/2x + 3

• x^2 - 2

• 2x - 3

• x + 3

What mistake was corrected in the second example?

• The wrong color was used for the second piece

• The wrong values were plotted for the first piece

• The wrong domain was used for the first piece

• The wrong rule was used for the second piece

In the third example, what is the rule for numbers greater than 1?

• x + 4

• 1/2x + 3

• x^2 - 4x + 4

• 3x + 13

For the third example, what type of circle is used at the point (1, 0) for the third rule?

• Open circle

• Closed circle

• No circle

• Dashed circle

In the third example, what is the rule for numbers between -4 and 1?

• 1

• 1/2x + 3

• x^2 - 4x + 4

• 3x + 13