Evaluating Piecewise Defined Functions

This video tutorial explains how to evaluate a piecewise-defined function for different values and analyze the intervals where the function is increasing or decreasing. The instructor demonstrates the evaluation process by identifying the correct formula for each interval and provides examples to illustrate the concept. Additionally, the video discusses how to determine the intervals where the function is increasing or decreasing without using a graph.

What is a piece-wise defined function?

• A function with a single formula for all x values.

• A function that only works for positive x values.

• A function that is broken up into pieces with different formulas.

• A function that is always increasing.

Which formula is used for x values less than or equal to -2?

• x + 1

• 3

• x^2

• x - 1

What is the value of f(-4)?

• 3

• 16

• -5

• -3

Which interval does the value 0 fall into?

• None of the above

• Between -2 and 1

• Greater than 1

• Less than or equal to -2

What is the value of f(4)?

• 4

• -4

• 16

• -16

For which interval is the function always 3?

• x less than or equal to -2

• x between -2 and 1

• None of the above

• x greater than 1

What happens to the function for x values greater than 1?

• It increases.

• It oscillates.

• It stays constant.

• It decreases.

What is the value of f(2)?

• -9

• 9

• -4

• 4

For which interval is the function increasing?

• x greater than 1

• x between -2 and 1

• None of the above

• x less than or equal to -2

What is the value of f(-3)?

• 0

• -1

• -2

• -4