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Absolute Value Review

1.) |5| = ? Answer: 5 2.) |-5| = ? Answer: 5 3.) |-10| = ? Answer: 10 4.) |0| = ? Answer: 0. 5.) |-x| = ? if x = -2 Answer: 2 6.) |x| - 3 = ? if x = -2 Answer: -1 7.) | x - 2| - 1 = ? if x = -2 Answer: 3 8.) -| x + 1| = ? if x = -2 Answer: -1. Absolute Value Review.

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Absolute Value Review

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  1. 1.) |5| = ? Answer: 5 2.) |-5| = ? Answer: 5 3.) |-10| = ? Answer: 10 4.) |0| = ? Answer: 0 5.) |-x| = ? if x = -2 Answer: 2 6.) |x| - 3 = ? if x = -2 Answer: -1 7.) |x - 2| - 1 = ? if x = -2 Answer: 3 8.) -|x + 1| = ? if x = -2 Answer: -1 Absolute Value Review

  2. Mon, 9/19 SWBAT… graph absolute value functions Agenda • Absolute value review (10 min) • Review problem from Friday (5 min) • Review HW#1/#2 (15 min) • Graphing absolute value functions (10 min) • Transformations of absolute value functions (5 min) HW#3: Absolute value functions and HW#4: Linear graphs & table of values application (due Wed)

  3. Test Corrections: Common spelling/ grammar mistakes • “I” should be capitalized • “supposed to” not suppose to • “Suppose” is a verb, meaning to think or to ponder. • The correct way to express a duty is to write, “I was supposed to…” • It’s “plugged” not pluged • It’s “parenthesis” • It’s “going to” not gonna • Even worse is “imma gonna” • Your vs. you’re • Their vs. there • “Their” is possessive; “there” refers to distance; and “they’re” is a contraction of “they are.”

  4. We have begun a new unit on functions: Cell phone project We will be able to: Know the Cartesian Coordinate System (HW1) Graph linear functions (equations) using a table of values (HW2) Graph absolute value functions (HW3) Interpret real life graphing examples (HW4) Graph piecewise value functions (HW5) Write and identify linear functions (HW6) Write algebraic equations given various forms of data (HW7) List the domain and range of a function (HW8) Determine if a relation is a function using the vertical line test or given a diagram (HW8) Evaluate a function and write as an ordered pair (HW8)

  5. Ex 2: Graph x – 2y = 5 using a table of values First Step: Solve for y (write y as a function of x) x – 2y = 5 –2y = -x + 5

  6. y x Second Step: Make a Table of Values

  7. Tues, 9/20 SWBAT… graph absolute value functions Agenda • Warm Up (5 min) • Transformations of linear functions (5 min) • Absolute value functions (20 min) • Transformations of absolute value functions (10 min) Warm-Up: How does the graph of y = x + 1 compare to the parent function graph, y = x? HW#3-Absolute value functions and HW#4-Linear graphs & table of values application

  8. The graph of the function y = x + 1 shifts 1 units up from the parent function, y = x. Q: How does the graph of y = -x – 2 compare to the parent function graph, y = x? A: The graph of the function y = -x – 2 is reflected across the x-axis and shifts 2 units down from the parent function, y = x.

  9. Absolute Value Function: A function in the form y = |mx + b| + c (m 0) Ex 1: Graph y = |x| by completing a table of values: Parent Function

  10. xy -2 -1 0 1 2 How does the graph of y = |x| – 3 transform from the parent function graph of y = |x| ? y = |x| – 3 is shifted 3 units down from the parent function, y = |x| Ex 2: Graph y = |x| – 3 by completing a table of values: y =|-2| –3= -1 y =|-1| –3= -2 y =|0| –3= -3 y =|1| –3= -2 y =|2| –3= -1

  11. Q: How would y = |x| + 5 transform from the parent function, y = |x|? A: The function y = |x| + 5 would shift 5 units up from the parent function, y = |x|.

  12. Reminders! More absolute value examples on-line HW3-Absolute value functions HW4-Tables of values application Review PPT3-Piecewise functions Tomorrow for 3rd period go to the Distance Learning Lab (next to the clinic)

  13. Thurs, 9/21 SWBAT… graph absolute value functions Agenda • Warm Up (10 min) • Absolute value functions (20 min) • Applications of TOV (15 min) Warm-Up: 1. -|x + 1| = ? if x = -2, x = -1, x = 0, x = 1, x = 2 2. How does the graph of y = |x + 1| compare to the parent function graph, y = x? (It does NOT shift up 1 unit!) 3. How does the graph of y = -|x + 1| compare to the parent function graph, y = x? Review PPT4 : Algebraic equations from data

  14. Warm-Up: #2 The graph of y = |x + 1| is shifted one unit to the left.

  15. xy -2 -1 0 1 2 y = -|x + 1| y = -|x + 1| is shifted 1 unit to the left and rotated around the x-axis from the parent function, y = |x| Ex 4: Graph y = -|x + 1| by completing a table of values: The vertex, or maximum point, is (-1, 0). y =-|-2 +1| = -1 y =-|-1+ 1| = 0 y =-|0 + 1| = -1 y =-|1 +1| = -2 y =-|2 +1| = -3

  16. Problem #3 y = SB

  17. xy -2 -1 0 1 2 y=|x –2| –1 y = |x – 2| – 1 is shifted 2 units to the right and 1 unit down from the parent function, y = |x| Ex 3: Graph y = |x – 2| –1 by completing a table of values: y =|-2 – 2| –1= 3 y =|-1 – 2| – 1= 2 y =|0 – 2| – 1= 1 y =|1 – 2| –1= 0 y =|2 – 2| – 1= -1 The vertex, or minimum point, is (2, -1).

  18. Q: How would y = |x + 4| + 3 transform from the parent function, y = |x|? A: The function y = |x + 4| + 3 would shift 4 units to the left and 3 units up from the parent function, y = |x|.

  19. #6 on HW3 Q: How would y = -|x + 1| + 3 transform from the parent function, y = |x|? A: The function y = -|x + 1| + 3 would shift 1 unit to the left shift, 3 units up, and rotate around the x-axis from the parent function, y = |x|.

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