Understanding Piecewise Defined Functions

This video tutorial explains how to analyze a piecewise defined function by examining its graph. It covers determining the domain and range using interval notation, evaluating specific function values, and identifying intercepts and zeros. The tutorial also discusses finding the minimum and maximum values of the function and analyzing its behavior over different intervals, such as increasing, decreasing, or constant.

What is the domain of the piecewise defined function in interval notation?

• [-3, 5)

• (-3, 5)

• [-3, 5]

• (-3, 5]

How is the range of a piecewise defined function determined?

• By analyzing the graph horizontally

• By analyzing the graph vertically

• By analyzing the graph diagonally

• By analyzing the graph circularly

What is the function value f(4) for the given piecewise defined function?

• 2

• -3

• 4

• 0

If f(x) = 1, what are the possible x values?

• 0 and 2

• -2.5 and 0.5

• 1 and 3

• -3 and 1

Where does the graph of the function intersect the y-axis?

• (0, 0)

• (0, 2)

• (2, 0)

• (1, 0)

What are the x-intercepts of the graph?

• (-3, 0) and (1, 0)

• (0, 3) and (0, 1)

• (3, 0) and (1, 0)

• (-1, 0) and (3, 0)

What is the minimum value of the function?

• -3

• 2

• 0

• -4

What is the maximum value of the function?

• 5

• 3

• 2

• 4

Over which interval is the function increasing?

• (-3, -2) and (3, 5)

• (-2, 0) and (0, 3)

• (0, 3) and (3, 5)

• (-3, 0) and (0, 2)

Over which interval is the function constant?

• (-3, -2)

• (-2, 0)

• (0, 3)

• (3, 5)