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# Writing, Graphing, and Describing Piecewise Linear Functions

Lesson 14 of 20

## Objective: SWBAT describe a piecewise function in their own words, graph it, and write equations modeling the graph.

#### Warm up

*10 min*

Today's Warm up is intended to take about 10 minutes for my students to complete and for me to review with the class. My students have worked with function notation before this lesson. We begin today's lesson with a review of how to evaluate a function, f(x) when given values for x. Then, students are asked to determine the value(s) of x that corresponds to a given output from a function.

In the video below, I demonstrate the strategy I use to teach graphing piecewise functions:

#### Resources

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#### Using a Piecewise Function

*15 min*

After reviewing the Warm Up with students, I hand each student an Activity called Running Errands from this website:

http://k12.wvu.edu/Courses/MathII/Unit%201/Lesson8/Activities/U1-L8-activity1.pdf

(last accessed 3-22-15)

I plan to have my students work on the activity individually for about 10 minutes. Then I will ask them to compare results with a table partner. For this activity the table partners are grouped homogeneously. I find that this helps my students to maintain the opportunity to think on their own, and share ideas with confidence.

While my students are working I am walk around the room monitoring their progress. Most of the students will be able to draw the five line segments on the graph associated with each of the five errands. However, I expect my students to have difficulty with the following elements of the task:

- writing the equation of each line correctly (with the slope and the y-intercept correct)
- understanding and using function notation correctly
- writing the domain correctly using inequality statements

When students share their work, I will emphasize the precise use of function notation (MP6).

Here are some examples of my students' work on this task:

- Student One uses 0 for the y-intercept in all of the equations, but does find the slope correctly. However writes the equations in slope intercept form, and uses function notation incorrectly by placing f of x equal to an inequality. Students should realize that f(x) is equivalent to y.
- Student Two did not finish. Student two wrote two equations horizontally that were correct. However, the student did not list the equations vertically next to each domain, and the student also numbered within the function notation. Again, emphasizing Math Practice six and the importance of writing function notation correctly.
- Student Three writes all of the equations correct except the slope and the y-intercept of the last line segment. However, this student also shows lack of understanding of f(x) because the student puts additional y= symbols inside the brackets.

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#### Guided Practice

*20 min*

After the Using a Piecewise Function activity, I will work through a Guided Practice with students. I will lead this segment of the lesson so that we can focus on some of the difficulties that students experienced during the first half of today's lesson.

I will begin by working some of the problems on the worksheet while the students observe. Then, I will give them time to produce graphs on their own. Earlier, I had demonstrated how to read a function definition and graph a Piecewise Function. During the Guided Practice, I focus more on the last page of Graphing Piecewise Functions where students interpret a graph and write a piecewise function to describe it. The video below contains is an example of how I might do this with my students:

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#### Exit Slip

*10 min*

With about ten minutes remaining in the period, I give the students an Exit Slip to check for comprehension. Some of the issues I will look for in my students' work on this informal assessment are:

- Did students restrict the domain appropriately or did they extend a graph(s) outside of its domain?
- Did students accurately plot open and a closed circles on the plot.
- Did students may have difficulty with slope or y-intercept.
- Did students incorrectly use function notation.

I have provided a copy of a correct graph in the resources.

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Sequences
- LESSON 2: The Recursive Process with Arithmetic Sequences
- LESSON 3: Recursive vs. Explicit
- LESSON 4: Increasing, Decreasing, or Constant?
- LESSON 5: Change Us and See What Happens!
- LESSON 6: Why are lines parallel?
- LESSON 7: Get Perpendicular with Geoboards!
- LESSON 8: Dueling Methods for Writing the Equation of a Line
- LESSON 9: Comparing Linear Combinations in Ax +By= C to y=mx +b
- LESSON 10: Equations for Parallel and Perpendicular Lines.
- LESSON 11: Assessment of Graphing Lines through Art!
- LESSON 12: Are x and y Directly or Inversely Proportional? (Day 1 of 2)
- LESSON 13: Are x and y Directly or Inversely Proportional? (Day 2 of 2)
- LESSON 14: Writing, Graphing, and Describing Piecewise Linear Functions
- LESSON 15: Introduction to Scatter Plots, Line of Best Fit, and the Prediction Equation
- LESSON 16: Predicting the Height of a Criminal (Day 1 of 2)
- LESSON 17: Predicting the Height of a Criminal (Day 2 of 2)
- LESSON 18: Predicting Bridge Strength via Data Analysis (Day 1 of 2)
- LESSON 19: Predicting Bridge Strength via Data Analysis (Day 2 of 2)
- LESSON 20: Linear Assessment