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Algebra 2 2-7 Complete Lesson: Absolute Value Functions and Graphs

By Matt Richardson
Last updated almost 3 years ago
28 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! You jog at a constant speed. Your jogging route takes you across the county line.

Suppose you graph your distance from the county line with respect to time. Which of the following graphs is most reasonable? Assume that your jogging route is a straight road.

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Problem 1 Got It? What is the graph of the function y = |x| + 2? Graph the function on the canvas. Use colors other than black.

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Problem 1 Got It: Graph the parent function and translated function on the same plane. Zoom and pan your graph to leave an appropriate scale and viewing window.

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Problem 1 Got It: How is the graph of y = |x| + 2 related to the graph of its parent function y = |x|?

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Problem 1 Got It? Reasoning: Do transformations of the form y + |x|+ k affect the axis of symmetry? Explain.

You may use this pre-made Desmos graph to analyze the effects of k on the parent function here. Drag the slider in the second row to see how different vales of k impact the graph.

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Problem 2 Got It? What is the graph of the function? Graph the function on the canvas. Use a color other than black.

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Problem 3 Got It? What is the graph of the function? Graph the function on the canvas. Use a color other than black.

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Problem 3 Got It? What is the graph of the function? Graph the function on the canvas. Use a color other than black.

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Problem 4 Got It?

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Problem 5 Got It?

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Reasoning: Is it true that without making a graph of an absolute value function, you can describe its position in the coordinate plane? Explain with an example function.

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Graphing: Graph two absolute value functions such that they have a common vertex in Quadrant III and one is the reflection of the other in a [across a] horizontal line. Graph the functions. Zoom and pan your graph to leave an appropriate scale and viewing window.

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Review Lesson 2-6: Write an equation for the transformation of the graph of y = x + 2.

2 units up, 3 units right

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Review Lesson 2-6: Identify the functions that correspond to f(x) = 2x - 6 after the indicated reflections.

  • f(x) = -2x + 6
  • f(x) = -2x - 6
  • Reflection across the y-axis
  • Reflection across the x-axis
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Review Lesson 2-5: Sketch a trend line for each scatter plot on the canvas. Use the line segment tool and colors other than black.

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Vocabulary Review: Simplify the absolute value expression. Enter only a number.

Vocabulary Review: Simplify the absolute value expression. Enter only a number.

Vocabulary Review: Simplify the absolute value expression. Enter only a number.

Vocabulary Review: Simplify the absolute value expression. Enter only a number.

Use Your Vocabulary: Draw a line of symmetry through each figure on the canvas.

Use Your Vocabulary Identify the graph that does NOT show symmetry about the y-axis.

  • Does NOT show symmetry about the y-axis

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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