1. SWBAT… graph piecewise and absolute value functions Agenda 1. Warm Up (15 min) 2. Absolute value and piecewise functions (30 min) Warm-Up: 1. Take out your absolute value and piecewise function notes 2. Take out hw#6 3. Write your hw in your planner for the week 4. Compare answers for the functions take home test (will be collected in 10 min) HW#6: Functions Mon, 11/29/10

2. Absolute Value Quick 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

3. Ex 1: Graph y = |x| by completing a table of values: x y -2 0 1 2 Absolute Value Function: A function in the form y = |mx + b| + c (m 0) y =|-2| = 2 y =|-1| = 1 y =|0| = 0 y =|1| = 1 y =|2| = 2 The vertex, or minimum point, is (0, 0).

4. Ex 2: Graph y = |x| – 3 by completing a table of values: x y -2 0 1 2 y =|-2| – 3= -1 y =|-1| – 3= -2 y =|0| – 3= -3 y =|1| – 3= -2 y =|2| – 3= -1 The vertex, or minimum point, is (0, -3).

5. y=|x – 2| – 1 The vertex, or minimum point, is (2, -1). Ex 3: Graph y = |x – 2| – 1 by completing a table of values: x y -2 0 1 2 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

6. y = -|x + 1| The vertex, or maximum point, is (-1, 0). Ex 4: Graph y = -|x + 1| by completing a table of values: x y -2 0 1 2 y =-|-2 +1| = -1 y =-|-1+ 1| = 0 y =-|0 + 1| = -1 y =-|1 +1| = -2 y =-|2 +1| = -3

7. Piecewise Function A piecewise function is any function that is in, well, pieces! Piecewise functions indicate intervals for each part of the function Graph f(x) =

8. f(x) = 1 x y Step 1: Graph f(x) = 1 Step 2 : Erase part of the graph where x >3 Step 3: Graph f(x) = x + 1 Step 4: Erase part of the graph where x<3 f(x) =

9. f(x) = {1 x < 3 x y 3 Step 1: Graph f(x) = 1 Step 2 : Erase part of the graph where x >3 Step 3: Graph f(x) = x + 1 Step 4: Erase part of the graph where x<3 f(x) =

10. f(x) = x + 1 x y Step 1: Graph f(x) = 1 Step 2 : Erase part of the graph where x >3 Step 3: Graph f(x) = x + 1 Step 4: Erase part of the graph where x<3 f(x) =

11. f(x) = {x+1 x > 3 x y 3 Step 1: Graph f(x) = 1 Step 2 : Erase part of the graph where x >3 Step 3: Graph f(x) = x + 1 Step 4: Erase part of the graph where x<3 f(x) =

12. Summary of Steps for our example f(x) = Step 1: Graph f(x) = 1 Step 2 : Erase part of the graph where x >3 Step 3: Graph f(x) = x + 1 Step 4: Erase part of the graph where x<3

13. More Examples Go to the following website for more examples on graphing piecewise functions: http://archives.math.utk.edu/visual.calculus/0/functions.1 3/index.html

14. The graph shows the monthly fee for Cell Zone. Use it to answer the following questions: 1) What is the monthly fee? 2) How many minutes are included in the monthly fee? 3) If a customer goes over the minutes included in the fee, how much will they be charged per minute ($/min)? 4) Write a function for this plan.