1. 2-4 A Variety of Graphs Piecewise Functions

2. What are Piecewise Functions? Piecewise functions are defined for specific domains. The most basic example of a piecewise function is the absolute value function.

3. Graphing absolute Values

4. How will we graph? We will find the vertex of the graph. and then plot 2 points on either side of the vertex. Why 2 points instead of just 1 on each side?

5. Graphing Absolute Value 1.Set the inside of the absolute value = 0; solve for x. Plug this x back in and solve for y. You now have the coordinates of the vertex. 2.Plug in 2 “x” values on each side of the vertex (equidistant works well) and make sure the corresponding y values are equal. (IF they aren’t, what have you just figured out?

6. Examples 1. Vertex (3,2) 2. Vertex (0,4) Graph faces down

7. The next kind of piecewise function The form of this function is similar to this: This looks worse than it is. Essentially the function is split into multiple functions based on particular domains. (you might only see 2 functions, you could see 4..)

8. There will be 3 graphs Plot 3 x/y charts (include the EP of each domain) x y x y x y 2 3 4 0 -1 1 2 2 5 0 -1 2 -2 4 Open circle on graph Closed circle on graph

9. Group Problem: Graph