SWBAT… graph piecewise functions

Agenda 1. Warm Up (10 min)2. Quiz (20 min)3. Graphing (15 min)

Warm-Up:1.) Turn in HW#7 in the blue folder2.) Review your graphing linear equations

using a table of values and absolute value notes including transformations

Review PPT3: Piecewise functions

Wed, 9/28

1.) Cut a piece of graph paper into 4 squares

2.) On one graph paper square: 1. Graph x = 32. Graph y = -2

3.) On another graph paper square, graph y = x + 1

Review PPT 3: Piecewise functions

SWBAT… graph piecewise functions

Agenda 1. Warm Up (10 min)2. Piecewise functions (35 min)

Warm-Up:1.) Cut a piece of graph paper into 6 squares2.) On one graph paper square:

1. Graph x = 32. Graph y = -2

3.) On another graph paper square, graph y = x + 1

Wed, 9/28

HW#5: Piecewise functions

Graphing Horizontal & Vertical Linesy

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 = 3Since there are no y–values in

this equation, x is always 3 and y can be any other real number.

x = 3

Graph y = –2Since there are no x–values in

this equation, y is always –2 and x can be any other real number.

y = –2

SWBAT… graph piecewise functions

Agenda 1. Warm Up (10 min)2. Piecewise functions (35 min)

Warm-Up:1.) On one graph paper square:

1. Graph x = -52. Graph y = 1

2.) On another graph paper square, graph y = x + 1

3.) On a number line graph x > 3

Thurs, 9/29

HW#5: Piecewise functions

y

x

Graph x = -5Since there are no y–values in this equation, x is always -5 and y can

be any other real number.

x = -5

Graph y = 1Since there are no x–values in this equation, y is always 1 and x can

be any other real number.

y = 1

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Step 2: Look at the Step 2: Look at the y-intercept (b)y-intercept (b) and plot where the graph crosses the and plot where the graph crosses the y-axis.y-axis.

Step 3: Use the Step 3: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot. Slope = 1 = Slope = 1 = 11//11

Step 4: Draw a line Step 4: Draw a line through both points. through both points. Be sure to extend the Be sure to extend the line and put arrows at line and put arrows at both ends. (Use a both ends. (Use a ruler!)ruler!)

y = x + 1

x

y

Step 5: Label your lineStep 5: Label your line

Step 1: Solve for yStep 1: Solve for y

Endpoints when graphing

< > ≤ ≥

Endpoints when graphing

< > ≤ ≥

Open Circle Open Circle Closed circle Closed circle

Piecewise Function A piecewise function is any function that is in, well, pieces! Piecewise functions indicate intervals for each part of the

function

1

1

x 3

3

x

xGraph f(x) =

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

1

1

x 3

3

x

xf(x) =

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

1

1

x 3

3

x

xf(x) =

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

1

1

x 3

3

x

xf(x) =

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

1

1

x 3

3

x

xf(x) =

Summary of steps for our example

f(x) =

1

1

x 3

3

x

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. 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.

100 200 300 400 500 600 700 800

Peak Minutes (minutes)

80 60 40 20

Fee ($)