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Algebra II Honors—Day 9

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Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students. You may choose your groups today, but you will need to work and not just socialize.

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Goals for Today Reminder—First Graded Homework Assignment (checked for accuracy)—due next Tuesday, Sept. 10 Quotable Puzzle due Monday, Sept. 9 Show me Domain/Range Homework to get homework stamp Essential Questions – New Material/Group Investigations Homework

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Warmup (in your notes) Given the functions : find the following:

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Essential Questions How do the values of a, b, c, and d in the function affect the graph of ?

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Exploring the Absolute Value Function The absolute value function is a function of the form It has a two-part definition as follows: for and for

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How to graph xy=|x| 11 22 4.6 1 -22 -3.53.5 For positive x- values, the y-values are the same For negative x- values, the y-values are the opposite sign

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The Graph For x≥0, the graph is the same as the line y=x (intercept of 0 and slope of POSITIVE 1) For x<0, the graph is the same as the line y=-x (intercept of 0 and slope of NEGATIVE 1) y=|x|

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Explanations f(x)=a|bx+c|+d The letters a, b, c, and d represent shifts or changes to the basic “parent” graph of f(x)=|x|. Each of these plays a different role in the movement of the graph. You will explore each.

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Assignment Within each group divide up the work in each section on the handout and then compare answers for all the parts. Use the whiteboards first until all graphs are finished. Draw the basic graph: f(x)=|x|. This is called the “parent graph” or the “parent function.” Make a table of points for the other equations and graph each one on the same coordinate plane. For each graph, use the domain {-3, -1, 0, 1, 3} and find the y-values. Then draw the graph.

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Homework Absolute Value Graphs – Do without a calculator based on what you learned. Problems 1, 2, 4, 7, 8, 9

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