section 2.6 special functions. i. constant function f(x) = constant example: y = 4 ii. identity...

Section 2.6

Special Functions

I. Constant functionf(x) = constant

Example:y = 4

II. Identity functionf(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 whereThey get their name

V. Greatest Integer Function

For any number x, rounded down to thegreatest integer not equal to x.

2

2

2.1 2

2

.

.

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 1 + 2 -1 -1 + 2

2 2 + 2 -2 -2 + 2

3 3 + 2 -3 -3 + 2

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) = $0.41 + $0.17[x - 1]

When the weight exceeds each integer valueof 1-ounce, the price increases by $0.17

WeightNot Over Single Piece(Ounces)

0 $0.001 $0.412 $0.583 $0.75

For letters ≥ 1-ounce

f(x) = $0.41 + $0.17[x - 1]

x f(x)

1

1.1

1.2

1.9...

2

2.1

For x(ounces) ≥ 1

Postage Fee

Homework

Practice Worksheet 2-6 and

Page 106

Problems: 20 - 28 (graphed on graph paper)