Piecewise+Functions


 * Goal:**


 * 1.** Understand how to graph and write an equation of a piecewise function


 * __Content Standard:__**

F.IF.7 Graph functions expressed symbolically and show key features of the graph, by and in simple cases and using technology.


 * Graph quadratic functions expressed in various forms by hand.
 * Use technology to model quadratic functions, when appropriate.
 * Graph and find key features of square root, cube root and piecewise-defined functions, including step functions and absolute value functions.


 * __Develop:__**

The following task is designed to introduce the concept of piece-wise functions.

Give each student a piece of graph paper. Instruct them to draw an x-axis and a y-axis. (The location of the axes is not important: they can be in the center so all four quadrants are shown, or in the corner so you only see one quadrant.) Instruct the student to fold the paper into four different sections (they can be equal sizes or different sizes). The folds should be made along the graph lines parallel to the y-axis.
 * Set-up:**

Step 1: Draw a point on the leftmost grid line. Draw a point on the first folded line, from left to right. Connect the two points.

Step 2: Draw a point on the second folded line and connect that point with the point on the first folded line.

Step 3: Repeat this process, drawing a point on the next folded line and connecting it to the point on the previous folded line until all four sections have a line segment in them.


 * Problem:** Create a function that describes the path that has been drawn.

(Optional: Students can exchange papers as they draw the line segments. The first student can even fold his section back so the next student can only see the ending point of his line but not the line itself)


 * __Solidify:__**

Task 2: One Moving Point (word document)

Solution:


 * __Practice:__**

Task 3: Two Moving Points (word document)

Solution: