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