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Algebra II Honors—Day 10

Algebra II Honors—Day 10. Procedures. Pick up the following from the table: Handout, whiteboard, marker, eraser Get into groups of three or four students. . Goals for Today. Reminder—First Graded Homework Assignment (checked for accuracy)—tomorrow—Tuesday, Sept. 10

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Algebra II Honors—Day 10

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  1. Algebra II Honors—Day 10

  2. Procedures • Pick up the following from the table: • Handout, whiteboard, marker, eraser • Get into groups of three or four students.

  3. Goals for Today • Reminder—First Graded Homework Assignment (checked for accuracy)—tomorrow—Tuesday, Sept. 10 • Quotable Puzzle due today • No homework check today • Essential Questions • New Material/Group Investigations • Homework

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

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

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

  7. 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.

  8. 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.

  9. The effect of “a” (the number outside the function—multiplies the entire function) The parent function • New function “grows” faster • called a “vertical stretch” • slope is steeper—multiplied by “a” • New function “grows” slower • called a “vertical shrink” • slope is less steep—multiplied by “a” • the negative flips it upside down as well

  10. The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only) The parent function • b=1 and c=3 • New function is shifted LEFT 3 units (“-c”) and slope is still the same as parent • b=1 and c=-5 • New function is shifted RIGHT 5 units (“-c”) and slope is still the same as parent

  11. The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only) The parent function • b=6 and c=3 • New function is shifted LEFT 1/2 unit (“-c/b”) and slope is multiplied by 6 (“b”) • b=3 and c=-9 • New function is shifted RIGHT 3 units (“-c/b”)and slope is multiplied by 3 (“b”)

  12. The effects of “d” (the number added outside the function) The parent function • d=8 • New function is shifted UP 8 units (“d”) • d=-6 • New function is shifted DOWN 6 units (“d”)

  13. In your notes • Make sure you can summarize the effects of each of the numbers a, b, c, and d in the equation . These numbers will be used throughout this course for other functions. • Understand that each of these numbers either “shifts” or “stretches” the parent function.

  14. Homework • Absolute Value Graphs • Do without a calculator based on what you learned. Problems 1, 2, 4, 7, 8, 9, 10, 12

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