section 2.6 special functions. i. constant function f(x) = constant example: y = 4 ii. identity...
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Section 2.6
Special Functions
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I. Constant functionf(x) = constant
Example:y = 4
II. Identity functionf(x) = x
Types of Special Functions
y = x
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III. A linear function in the form f(x) = mx + b with b = 0, is called a direct variation function
y = mx+0
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IV. Step functions
Step functions are related
to linear functions
You can see whereThey get their name
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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
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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
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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
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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
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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
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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
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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
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Homework
Practice Worksheet 2-6 and
Page 106
Problems: 20 - 28 (graphed on graph paper)