Graphing Absolute Value Functions (Day 2 of 2)

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Objective

SWBAT graph absolute value functions on a coordinate plane.

Big Idea

Students will be introduced to the general formula of an absolute value function and use it to graph and make transformations two functions on the coordinate plane.

Do-Now

10 minutes

Students begin today's lesson by working on the Do Now. After about 5 minutes, student volunteers will come up to the board to draw a rough sketch of their graph on the board. We will verify the graphs using a thumb up/down/middle poll as a whole group.

Next, a student will read the objective, "SWBAT graph absolute value functions on a coordinate plane".

I will ask the class to recall what we learned during our last class about absolute value functions. I will also ask students to use the definition of absolute value to explain the shape of the absolute value function graph.

Introduction + Guided Notes

30 minutes

I will begin our lesson using Desmos to demonstrate the behavior of some absolute value functions. I will spend a few minutes graphing various absolute value functions that students volunteer as examples. We'll discuss each graph, where it is on the plot, its shape, etc. We'll do this informally to re-acclimate students to the absolute value function transformations that were discussed yesterday.

Next, I ask my students to graph a pair of absolute value functions from their Guided Notes.

f(x) = |x - 2| + 1

g(x) = -2|x| + 3

I expect most of my students will be able to identify the location of the vertex, but they will use the input/output table to verify additional points on the line. Additionally, students will also be able to better understand the the behavior of the vertex after completing the table. I will help students evaluate both functions for two to three points to ensure that their simplification is correct. Then I will students to finish completing the table and graph the function with a neighbor.

Next, I will ask students to decide the pros and cons of using a table to graph a function. Most students will immediately agree that this method can be tedious. I will ask students to analyze the table and the equation and decide which elements of the equation seem to be the most crucial when graphing an absolute value equation. After a brief discussion, I will introduce students to the general formula of an absolute value equation, f(x) = a|x-h|+ k. I will ask students to use what we have seen in class to decide the significance of a, h, and k.

I will lead students through the process of graphing an absolute value function with the example problems on page two and three. Students will complete page four with a partner. Lastly, student volunteers will come up to the board to demonstrate the sketch of their graphs to the class.

Group Activity: Matching

30 minutes

Students will practice what they have learned about absolute value functions with this Activity. Students will work with a partner to match the graph of an absolute value function to its equation, vertex, slope, domain, and range. This activity can be cut up by students, or completed without cutting. Many of my students prefer not to cutout the cards for this activity due to the number of cards that would result. 

When students have finished, they should record their answer on the table on page 4 of the activity. I only require my students to write the letter of the corresponding answer in the table. This makes it easier for me to scan and check answers.

Eventually, I will ask pairs to share their responses with the entire group. 

Closing

10 minutes

I will ask students to reflect on the work that was done in today's class. Next, I will ask students to reflect on the equation of an absolute value function and to decide if there will ever be an absolute value function where the "V" shape is pointing sideways. I will ask students to justify their knowledge of functions, as well as with a table or a sketch. Lastly, I will ask students to think about the similarities and differences between the graphs of linear and absolute value equations.

Students will then complete an Exit Card before leaving for the day.