Graphing and Evaluating Piecewise Functions

This video tutorial covers the basics of piecewise functions, focusing on linear and constant types. It explains what piecewise functions are, how to evaluate them by substituting values into the correct function piece, and how to graph them using slopes and y-intercepts. The tutorial also includes examples of writing equations and domains from graphed piecewise functions, emphasizing the importance of understanding restricted domains and using point-slope form for linear equations.

What defines a piecewise function?

• A function defined by multiple equations over different intervals.

• A function that can only be defined by a single equation.

• A function that has no breaks or intervals.

• A function that cannot be graphed.

How do you evaluate a piecewise function at a specific point?

• Always use the first equation given.

• Piecewise functions cannot be evaluated at specific points.

• Sum up all the function values.

• Use the equation that corresponds to the interval the point falls in.

What is the slope of the line defined by the equation -2x + 4?

• -2

• -4

• 4

• 2

How do you determine which part of a piecewise function to use when evaluating a point?

• Piecewise functions cannot evaluate specific points.

• By evaluating all parts and choosing the highest value.

• By always choosing the first function listed.

• By determining which domain the point falls into.

When graphing a piecewise function, what is important to note about the y-intercept?

• It determines the slope of the function.

• It is irrelevant for piecewise functions.

• It is always the highest point on the graph.

• It may not be included in the domain.

What does an open dot on a graph of a piecewise function signify?

• The point is where two functions intersect.

• The point is an error in the graph.

• The point is the highest value of the function.

• The point is not included in the function.

How is a constant function represented in a piecewise function?

• It cannot be part of a piecewise function.

• As a horizontal line over its domain.

• With a slope of 1.

• As a vertical line.

For a piecewise function, how do you graph a line with a slope of -1 and y-intercept at -6?

• Start at 6 on the y-axis and go up 1 unit for every 1 unit moved to the left.

• It cannot be graphed as described.

• Start at -6 on the x-axis and go up 1 unit for every 1 unit moved to the right.

• Start at -6 on the y-axis and go down 1 unit for every 1 unit moved to the right.

What is the correct way to write the domain of a function that includes -2 but not 2?

• (-2, 2)

• [-2, 2)

• (-2, 2]

• [-2, 2]

What is the value of a piecewise function at a point where the domain changes?

• It depends on the function definitions and their domains.

• It is always 0.

• It is the sum of the values of all functions at that point.

• It is undefined.