Evaluating and Graphing Piecewise Functions

The video tutorial introduces piecewise functions, explaining their structure and how they are defined by different pieces. It covers evaluating these functions based on input values and demonstrates graphing them, highlighting the importance of understanding which piece to use for specific inputs. The tutorial emphasizes the continuity of piecewise functions and provides a visual representation of how they are graphed.

What defines a piecewise function?

• A function with uniform behavior across its domain

• A function defined by multiple sub-functions, each with its own domain

• A function that can only be defined graphically

• A function without any discontinuities

How do we determine which piece of the function to use for a given input?

• By calculating the limit as x approaches the input value

• By graphing the function

• By checking the input against the domain of each piece

• By evaluating the function's derivative

What is the value of the function when x is greater than 3?

• -1

• 0

• 3

• 1

What is the value of the function when x = 0?

• 1

• 2

• 0

• -1

For x = -1, which piece of the function is used?

• The piece for x > 3

• The piece for x < -2

• The piece for -2 < x < 2

• The piece for x = 0

How is the graph of the function for x < -2 described?

• Linear

• Logarithmic

• Quadratic

• Exponential

What does the identity piece of the function represent?

• x = y for all x between -2 and 2

• x = y^2 for all x

• x = y for x < -2

• x = y for x > 2

What characteristic does the graph have for x > 2?

• It has a negative slope

• It has a positive slope

• It is vertical

• It is horizontal

Is the piecewise function continuous?

• It cannot be determined

• Yes, but only in certain sections

• No, it has discontinuities

• Yes, it is continuous everywhere

What does it mean for a function to 'own' an endpoint?

• The function is discontinuous at that endpoint

• The endpoint is a critical point

• The endpoint is an asymptote

• The function has a defined value at that endpoint