Evaluating Piecewise Functions and Their Graphs

The video tutorial explains piecewise functions, focusing on their evaluation and graphing. It begins with an introduction to piecewise functions and their conditions. The instructor then demonstrates how to evaluate these functions at specific points, using examples to clarify the process. The tutorial proceeds to graph piecewise functions, emphasizing the importance of using tables to plot points accurately. Finally, the video covers graphing linear functions, highlighting the significance of conditions in determining graph behavior.

What is the condition for using the first formula in the piecewise function?

• When x is equal to 1

• When x is less than 1

• When x is greater than or equal to 1

• When x is greater than 1

Which formula should be used when x is equal to 1?

• The first formula

• The second formula

• Both formulas

• Neither formula

What is the value of f(-1) for the given piecewise function?

• 1

• -1

• -1/2

• 1/2

What is the value of f(1) for the given piecewise function?

• 3

• 2

• 4

• 1

What is the value of f(sqrt(9/10)) for the given piecewise function?

• -9/20

• -1/2

• 9/20

• 1/2

How many points are needed to graph the quadratic part of the piecewise function?

• 2

• 4

• 3

• 1

What is the y-coordinate of the point when x = 0 for the quadratic part?

• 1

• 0

• -1/2

• 1/2

How many points are needed to graph the linear part of the piecewise function?

• 2

• 4

• 1

• 3

What is the y-coordinate of the point when x = 2 for the linear part?

• 3

• 4

• 6

• 5

What type of circle is used to represent a point that is included in the graph?

• Closed circle

• Dashed circle

• Open circle

• Solid circle