Step functions Greatest integer functions Piecewise functions 2.6 Special Functions Step functions Greatest integer functions Piecewise functions

The Constant Function Here f(x) is equal to one number. f(x) = 3. Have we seen this before?

Absolute Value function: f(x) = | x | Let plot some points x f(x) 0 0 1 1 -1 1 2 2 -2 2

Absolute Value function: f(x) = | x | Let plot some points x f(x) 0 0 1 1 -1 - 1 2 2 -2 - 2 Shape V for victory

Lets graph f(x) = - | x – 3| x - | x – 3| f(x) 0 - | 0 – 3| = - | - 3| - 3 (0, - 3) 1 - | 1 – 3| = - | - 2| - 2 (1, - 2) 2 - | 2 – 3| = - | - 1| - 1 (2, - 1) 3 - | 3 – 3| = - | - 0| 0 (3, 0) 4 - | 4 – 3| = - | 1 | - 1 (4, - 1) 5 - | 5 – 3| = - | 2 | - 2 (5, - 2)

Lets graph f(x) = - | x – 3| (0, - 3) (1, - 2) (2, - 1) (3, 0) (4, - 1) (5, - 2)

CW 2-5 Page 104 #8-11

Piecewise Functions Graphing different functions over different parts of the graph. One part tells you what to graph, then where to graph it. What to graph Where to graph

Piecewise Functions 2 is where the graph changes. Less then 2 uses 3x + 2 Greater then 2 uses x - 3

We can and should put in a few x into the function If f(0) we use 3x + 2, then 3(0) + 2 = 2 If f(3) we use x – 3, then (3) – 3 = 0 The input tell us what function to use.

We can and should put in a few x into the function If we want to find out what f(2) = we use both equations, but leaving an open space on the graph for the point in the function 3x + 2. Why?

We can and should put in a few x into the function f(2) in 3x + 2; 3(2) + 2 = 8 Graph an open point at (2,8). f(2) in x – 3 (2) – 3 = -1 Graphs a filled in point at (2, -1)

Piecewise Functions So put in an x where the domain changes and one point higher and lower (2, 8) (2, -1)

Graph the piecewise function

Write the Piecewise-defined Function

CW 2-6 (Cont.) Page 105 # 12-16

HW 2-6 #’s 17-19, 24-30