Lesson 6: 3-7 Piecewise and Step Functions
Duration of Days: 2
Lesson Objective
Desmos (reading and analyzing)
Identify and graph step functions.
Identify and graph piecewise-defined functions.
How do step and piecewise-defined functions help us to understand data sets?
step function
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
SAT questions related to slope: 8-3-13,6-3-1,5-4-7,8-3-19,7-4-17,1-3-6,3-4-8;
graphing: 6-3-5;
functions: 3-4-4, 5-4-2, 6-4-25
One type of step function is the greatest integer function. Other functions closely related to linear functions are the piecewise functions. Piecewise-defined functions are functions that are defined by two or more equations.
A taxi company charges a fee for waiting at a rate of $0.75 per minute or any fraction thereof. Draw a graph that represents this situation.
If students have trouble picturing the graphs of piecewise and step functions, then have students draw a large coordinate grid on two sheets of inch-grid paper. Students should use scissors, tape or glue, and straws to model the general shape of a step function and a piecewise-defined function. Have students label each type of graph.
Practice: Exercises 1-7
Exercises 41- 45
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