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Algebra 1 5-8 Complete Lesson: Graphing Absolute Value Functions

By Matt Richardson
Last updated almost 3 years ago
27 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! Write the equation of Line 1 in slope-intercept form.

Solve It! Write the equation of Line 2 in slope-intercept form.

Solve It! How can you transform the equation of Line 1 into the equation of Line 2? Explain.

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Solve It! How can you slide Line 1 in the coordinate plane so that it becomes Line 2? Explain.

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Vocabulary: In your own words, define translation.

Graphing: Graph the absolute value function. Zoom and pan your graph to establish an appropriate viewing window.

Problem 1 Got It? How is the graph shown related to the graph of y = |x|?

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Problem 1 Got It? Reasoning: Match the domains and ranges on the left with the appropriate function(s) on the right from Problem 1. Not all domains and ranges will be used.

  • D: All real numbers
  • R: All real numbers
  • D: [0, ∞)
  • R: [0, ∞)
  • R: [-2, ∞)
  • y = |x|
  • y = |x| - 2

Problem 2 Got It?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

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Problem 3 Got It?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

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Problem 4 Got It? Make a graph that models the relationship between the number of students x that go to the game by bus and the number of busses y that are needed if each bus holds a maximum of 50 students.

Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

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How is the graph of y = |x| - 8 different from the graph of y = |x|?
How is it the same?

After responding, you may check your answer using Desmos below. If you must edit your response, consider also editing your note card.

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What is the equation for the translation of y = |x| 9 units up?
You may check your response using Desmos.

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What is the graph of the function?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

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Compare and Contrast: How are the graphs of y = |x| - 4 and y = |x - 4| the same? How are they different?

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Error Analysis: A student is graphing the equation y = |x - 10| and translates the graph of y = |x| 10 units left. Describe her error.

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Reveiw Lesson 5-7: Write an equation of a trend line or use a graphing calculator to find an equation of the line of best fit.

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Reveiw Lesson 5-7: Write an equation of a trend line or use a graphing calculator to find an equation of the line of best fit.

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Review Lesson 5-3: Graph the equations on the same coordinate plane using the colors indicated for each.

Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

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Vocabulary Review: Compare the absolute values using the symbols on the left.

  • <
  • >
  • =
  • |3| _?_ |-3|
  • |-3| _?_ |-1|
  • |9| _?_ |-10|
  • |-9| _?_ |8|

Vocabulary Review: The absolute value of a number is a measure of the distance from 0 to that number on the number line.

Vocabulary Review: The absolute value of a number is always the opposite of that number.

Use Your Vocabulary: Classify the pair of figures.

Use Your Vocabulary: Classify the pair of figures.

Use Your Vocabulary: Classify the pair of figures.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

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