2 6 Special Functions Constant Function A linear

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2. 6 Special Functions

2. 6 Special Functions

Constant Function: A linear function in the form y = b. y = 3

Constant Function: A linear function in the form y = b. y = 3

Graph the following constant functions: Graph y = -2 Graph x = 4

Graph the following constant functions: Graph y = -2 Graph x = 4

Identity Function: A linear function in the form y = x. y=x

Identity Function: A linear function in the form y = x. y=x

A piecewise function consists of different function rules for different parts of the domain.

A piecewise function consists of different function rules for different parts of the domain. Graph the following function: ample 1 x y 6 5 4 3 2 1 1 2 3 4 5 6

Example 2 Graph the following function: 4 x y 6 x y

Example 2 Graph the following function: 4 x y 6 x y

Practice Graph the following function: x<1 x>1 x y

Practice Graph the following function: x<1 x>1 x y

Graph the piecewise function: 7 x 8 x y y

Graph the piecewise function: 7 x 8 x y y

Step Functions A step function is a piecewise function that consists of different constant

Step Functions A step function is a piecewise function that consists of different constant range values for different intervals of the domain of the function. Greatest integer function Rounding-down function 3 2 1 -3 -2 -1 -1 -2 -3 f(x) = [[x]] 1 2 3 x y

Graph y = [x] + 2 by completing the t-table: x --3 - 2.

Graph y = [x] + 2 by completing the t-table: x --3 - 2. 75 -2. 25 -2 -1. 75 -1. 25 -1 0 1 y y= [-3]+2=-1 y= [-2. 75]+2=-1 y= [-2. 25]+2=-1 y= [-2]+2 =0 y= [-1. 75]+2=0 y= [-1. 25]+2=0 y= [-1]+2=1 y= [0]+2=2 y= [1]+2=3 y 6 4 2 – 6 – 4 – 2 – 4 – 6 2 4 6 x

Example 1 Graph the following function: f(x) = 2 [[x-2]] x x y y

Example 1 Graph the following function: f(x) = 2 [[x-2]] x x y y

Graph the step function: g(x) = [[x+1]] -2 x x y y

Graph the step function: g(x) = [[x+1]] -2 x x y y

Absolute Value Function: A function in the form y = a|mx + b| +

Absolute Value Function: A function in the form y = a|mx + b| + c (m 0) Example #1 Y =|x - 2|-1 The vertex, or minimum point, is (2, -1).

Example 1 Graph the following function: x y

Example 1 Graph the following function: x y

Practice Graph the following function: f(x) = -3│x - 4│ x y

Practice Graph the following function: f(x) = -3│x - 4│ x y

Practice Graph the following function: x y

Practice Graph the following function: x y