Chapter 2: Functions and Graphs

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Chapter 2 Functions and Graphs
PART 2
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Increasing Decreasing Function
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Many type of Function
1. LINEAR FUNCTION
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2. Polynomial
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EXAMPLE
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3. Power Function
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ii. a1/n, n is a positive integer
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iii. a-1
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4. Rational Function
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5. Algebraic Function
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6. Trigonometri Function

• f(x)sin x ? means the sine of the angle whose
  radian measure is x

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properties
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6. Exponential Function
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7. Logarithmic Function
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8. Trancendental Function

• ? are functions that are not algebraic
• ? includes trigonometric, inverse
  trigonometric, exponential, logarithmic function

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Ex

• Classify the following functions as one of the
  types of functions !

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Answer
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Transformations of Funstions
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Stretching Reflecting
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Combinations of Functions
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OPERATIONs On FUNCTIONs

• Given skalar real a and function f,g then the
  definition of the function operation is given by
  
• (fg)(x) f(x) g(x)
• (f-g)(x)f(x) - g(x)
• (af)(x) a f(x)
• (f.g)(x) f(x)g(x)
• (f/g)(x) f(x)/g(x), g(x)?0
• Each domain function above is the intersection Df
  and Dg except for f /g

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• If find the functions
  fg, f-g, fg, f/g and the domain

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Composite function
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Composition Function

• Compositon function from function f and g, is
  denoted by f?g thus (f ?g)(x)f(g(x))
• With domain function

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Ex
if
Find each function and its domain!
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Given then find a. f g , f - g , f
.g , and f/ g b. Each the domain function !

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One to One Function
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• Is the function one to one?

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Graph!
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Inverse Function
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Cancellation Law
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