Graphing Piecewise Functions in Algebra 1

Mrs. Velez teaches how to graph and identify piecewise functions. The lesson covers breaking functions into pieces, using a calculator to graph them, understanding inequality symbols, and analyzing domain and range. Students learn to plot points, connect graphs, and evaluate functions at specific points. The lesson concludes with a final example and encourages students to assess their understanding.

What is the first step in identifying a piecewise function?

• Breaking it into different pieces

• Checking if it passes the horizontal line test

• Calculating the slope

• Finding the range

How do you determine if a graph represents a function?

• It has a positive slope

• It passes the vertical line test

• It is continuous

• It passes the horizontal line test

What is the purpose of setting up a table of points for a piecewise function?

• To check for continuity

• To determine the range

• To find the slope

• To identify the x-values to be used for graphing

When graphing the first piece of a function, what should you do after entering the function into the calculator?

• Calculate the slope

• Check for continuity

• Copy down the corresponding points

• Find the range

What does a closed circle on a graph indicate?

• The function has a positive slope

• The function is continuous

• The point is part of the function

• The point is not part of the function

How do you represent a point that is not part of the function on a graph?

• With a solid line

• With a dashed line

• With a closed circle

• With an open circle

What is the domain of a piecewise function?

• The set of all x-values

• The set of all y-values

• The range of the function

• The slope of the function

How do you handle gaps in the range of a piecewise function?

• Ignore them

• Combine the ranges into one continuous range

• Represent each piece of the range separately

• Use a dashed line to connect the gaps

When evaluating a piecewise function at a specific point, which point should you consider if there is an open and a closed circle?

• Neither point

• The open circle

• Both points

• The closed circle

What is the correct y-value for f(3) if the corresponding x-value has a closed circle?

• 4

• 6

• 0

• 2