SWBAT… graph piecewise functions Wed, 9/28 SWBAT… graph piecewise functions Agenda Warm Up (10 min) Quiz (20 min) Graphing (15 min) Warm-Up: 1.) Turn in HW#7 in the blue folder 2.) Review your graphing linear equations using a table of values and absolute value notes including transformations Review PPT3: Piecewise functions

2.) On one graph paper square: 1. Graph x = 3 2. Graph y = -2 1.) Cut a piece of graph paper into 4 squares 2.) On one graph paper square: 1. Graph x = 3 2. Graph y = -2 3.) On another graph paper square, graph y = x + 1 Review PPT 3: Piecewise functions

SWBAT… graph piecewise functions Wed, 9/28 SWBAT… graph piecewise functions Agenda Warm Up (10 min) Piecewise functions (35 min) Warm-Up: 1.) Cut a piece of graph paper into 6 squares 2.) On one graph paper square: 1. Graph x = 3 2. Graph y = -2 3.) On another graph paper square, graph y = x + 1 HW#5: Piecewise functions

Graphing Horizontal & Vertical Lines y x When you are asked to graph a line, and there is only ONE variable in the equation, the line will either be vertical or horizontal. For example … Graph x = 3 y = –2 Since there are no y–values in this equation, x is always 3 and y can be any other real number. Graph y = –2 Since there are no x–values in this equation, y is always –2 and x can be any other real number. x = 3

SWBAT… graph piecewise functions Thurs, 9/29 SWBAT… graph piecewise functions Agenda Warm Up (10 min) Piecewise functions (35 min) Warm-Up: 1.) On one graph paper square: 1. Graph x = -5 2. Graph y = 1 2.) On another graph paper square, graph y = x + 1 3.) On a number line graph x > 3 HW#5: Piecewise functions

Graph x = -5 Graph y = 1 y = 1 x = -5 Since there are no y–values in this equation, x is always -5 and y can be any other real number. y = 1 Graph y = 1 Since there are no x–values in this equation, y is always 1 and x can be any other real number. x = -5

Graph y = x + 1 Step 1: Solve for y Step 2: Look at the y-intercept (b) and plot where the graph crosses the y-axis. y = x + 1 y Step 3: Use the slope (rise/run) to determine the next point and plot. Slope = 1 = 1/1 x Step 4: Draw a line through both points. Be sure to extend the line and put arrows at both ends. (Use a ruler!) Step 5: Label your line

Endpoints when graphing < > ≤ ≥

Endpoints when graphing < > ≤ ≥ Open Circle Closed circle

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

Step 1: Graph f(x) = 1 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 y f(x) = f(x) = 1 x

Erase part of the graph where x >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 y f(x) = f(x) = {1 x < 3 x 3

f(x) = x + 1 Step 3: Graph f(x) = x + 1 Step 1: Graph f(x) = 1 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 y f(x) = x + 1 f(x) = x

Erase part of the graph where x<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 y f(x) = f(x) = {x+1 x > 3 x 3

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

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

The graph shows the monthly fee for Cell Zone 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. $40 400 minutes (60 – 40) / (600 – 400) = $0.10/min. This is slope (rate of change), meaning for every minute I talk (after 400 minutes), I will be charged $0.10. f = Fee m = Total minutes f(m) = 40 m ≤ 400 40 + 0.10(m-400) m > 400 17