The video tutorial explains how to graph piecewise functions, which are functions composed of multiple sub-functions, each with its own domain. The instructor demonstrates graphing techniques for linear and quadratic functions, emphasizing the importance of understanding constraints and using open or closed circles to indicate domain boundaries. The tutorial also covers how to combine these graphs into a single piecewise function while ensuring the graph passes the vertical line test.

What is a piecewise function?

• A function that does not have any constraints

• A function that is always linear

• A function composed of two or more sub-functions

• A function with only one expression

When graphing a piecewise function, what is the first step?

• Graph all functions together

• Start with the most complex function

• Graph each sub-function separately

• Ignore the constraints

How do you determine which part of a piecewise function to graph?

• By considering the constraints on X values

• By looking at the Y values

• By graphing all parts regardless of constraints

• By using only the first sub-function

Why is it important to graph each function separately before combining them?

• To make the graph look more complex

• To ensure each function is graphed correctly

• To save time

• To avoid using constraints

What is the significance of an open circle in a piecewise graph?

• It marks the end of the graph

• It shows the function is continuous

• It represents a point included in the function

• It indicates the function is undefined at that point

What does a closed circle on a graph indicate?

• The point is included in the function

• The function is undefined at that point

• The graph ends at that point

• The point is not part of the function

How do you handle multiple constraints in a piecewise function?

• Graph all functions without considering constraints

• Graph each function separately and erase parts not meeting constraints

• Ignore constraints and graph the entire function

• Use only the first constraint for all functions

What is the purpose of the vertical line test in graphing?

• To check if the graph is a straight line

• To ensure the graph represents a function

• To verify the graph is symmetrical

• To confirm the graph is continuous

What should you do if a piecewise function does not pass the vertical line test?

• Adjust the constraints to ensure it passes

• Re-graph the function without constraints

• Add more functions to the piecewise function

• Ignore the test and proceed

What is the final step in graphing a piecewise function?

• Ignore the constraints

• Graph each function separately

• Apply the constraints to the combined graph

• Erase the entire graph