Section 2.6 Special Functions

I. Constant function f(x) = constant Example: y = 4 II. Identity function f(x) = x Types of Special Functions y = x

III. A linear function in the form f(x) = mx + b with b = 0, is called a direct variation function y = mx+0

IV. Step functions Step functions are related to linear functions You can see where They get their name

V. Greatest Integer Function For any number x, rounded down to the greatest integer not equal to x x f(x) = [ x ] [ x ] 2.9 symbol

VI. Absolute Value Functions The absolute value is described as follows: If x is “+” the absolute value of x is +x If x is “ - ” the absolute value of x is +x f(x) =  x 

1.) Graph: f(x) =  x + 2  x  x + 2  f(x) 1     2   -2   3   -3  

2.) Graph: f(x) =  x  +2 3.) Graph: f(x) =  x - 2  5.) Graph: f(x) =  x - 2  +2 4.) Graph: f(x) = 2  x 

6.) f(x) = 2 [ x ] 7.) f(x) = [ x - 2 ] 9.) f(x) =  x - 2  -3 8.) f(x) = [ x ] +3 State the transformation for each

10.) When you send a letter, the number of stamps you need is based on weight. f(x) = $ $0.17[x - 1] When the weight exceeds each integer value of 1-ounce, the price increases by $0.17 For letters ≥ 1-ounce

f(x) = $ $0.17[x - 1] xf(x) For x(ounces) ≥ 1 Postage Fee

Homework Practice Worksheet 2-6 and Page 106 Problems: (graphed on graph paper)