Algebra 2 2-7 Guided Practice: Absolute Value Functions and Graphs

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Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! You jog at a constant speed. Your jogging route starts a certain distance away from the county line. You approach the line, cross it, and continue past it and into the next county.

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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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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Sketch the graph of the parent absolute value function on the canvas.

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Take Note: Define axis of symmetry.

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Take Note: Sketch the axis of symmetry on the absolute value function graphed on the canvas. Use a bright color.

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Take Note: Define vertex (of the graph of an absolute value function).

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Take Note: Circle the vertex of the absolute value function graphed on the canvas. Use a bright color.

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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: 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. Drag the slider in the second row to see how different values of k impact the graph.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Match each general form of a transformation of the parent absolute value function on the left with the type of transformation it represents.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Draggable item		Corresponding Item
y=a\|x\|, \ a>1		Reflection in the x-axis
y=-\|x\|		Reflection in the y-axis
y=\|x\|+k, \ k>0		Vertical stretch
y=\|x\|-k, \ k>0		Vertical compression
y=\|x+h\|, \ h>0		Horizontal translation right
y=a\|x\|, \ 0<a<1		Horizontal translation left
y=\|-x\|		Vertical translation up
y=\|x-h\|, \ h>0		Vertical translation down

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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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Video Check: Select all that apply with regards to the video embedded directly above this item.

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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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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Consider the general form of the absolute value function y=a|x-h|+k.
Match each item on the left with the element of the graph of the function that it represents or causes.

Draggable item		Corresponding Item
h		The vertex of the graph of the function
x=h		The axis of symmetry of the graph of the function
(h,k)		Vertical stretch or compression
a		Horizontal translation
k		Vertical translation

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Problem 4 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Problem 5 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Sketch the graph of the parent absolute value function on the canvas.

Take Note: Define axis of symmetry.

Take Note: Sketch the axis of symmetry on the absolute value function graphed on the canvas. Use a bright color.

Take Note: Define vertex (of the graph of an absolute value function).

Take Note: Circle the vertex of the absolute value function graphed on the canvas. Use a bright color.

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.

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

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. Drag the slider in the second row to see how different values of k impact the graph.

Video Check: Select all that apply with regards to the video embedded directly above this item.

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

Video Check: Select all that apply with regards to the video embedded directly above this item.

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

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

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider the general form of the absolute value function y=a|x-h|+k.Match each item on the left with the element of the graph of the function that it represents or causes.

Problem 4 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 5 Got It?

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

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.

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. Drag the slider in the second row to see how different values of k impact the graph.

Take Note: Consider the general form of the absolute value function y=a|x-h|+k.
Match each item on the left with the element of the graph of the function that it represents or causes.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?