Graphing Piecewise Functions: Key Concepts and Techniques

The video tutorial covers the graphing of piecewise functions, starting with an introduction to the concept and setup of three equations. It then demonstrates how to graph each function individually, explaining the use of open and closed circles based on inequalities. The tutorial concludes with a detailed explanation of domain and range using interval notation, and a recap of the key points covered.

What are the three equations used in the piecewise function?

• y = x + 2, y = 2x + 5, y = -x + 1

• y = x + 1, y = 2x + 4, y = -x + 0

• y = x - 2, y = 2x - 5, y = -x - 1

• y = x + 3, y = 2x + 6, y = -x + 2

For the first piecewise function, what type of circle is used at x = 0?

• Closed circle

• Open circle

• Half-filled circle

• No circle

What is the y-value when x = -1 for the first piecewise function?

• 2

• 0

• 1

• -1

What are the x-values used to graph the middle piecewise function?

• 2 and 3

• 0 and 2

• 0 and 1

• 1 and 2

What is the y-value when x = 2 for the middle piecewise function?

• 11

• 9

• 7

• 5

For the last piecewise function, what is the y-value when x = 3?

• -1

• -2

• -3

• -4

What type of circle is used at x = 2 for the last piecewise function?

• No circle

• Half-filled circle

• Open circle

• Closed circle

What is the domain of the piecewise functions?

• 0 to 2

• 5 to 9

• Negative infinity to infinity

• Negative infinity to 2

What is the range of the piecewise functions?

• 5 to 9

• Negative infinity to 2 and 5 to 9

• 0 to 9

• Negative infinity to 0

Why is interval notation preferred for domain and range?

• It is easier to read

• It is more precise

• It is more commonly used

• It is required by the teacher