🗊Презентация Functions and graphs. Chapter 2. Combinations of functions; composite functions

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Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №1Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №2Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №3Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №4Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №5Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №6Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №7Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №8Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №9Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №10Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №11Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №12
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Functions and graphs. Chapter 2. Combinations of functions; composite functions, слайд №1
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Objectives: Find the domain of a function. Combine functions using the algebra of functions, specifying domains. Form composite functions. Determine domains for composite functions. Write functions as compositions.
Описание слайда:
Objectives: Find the domain of a function. Combine functions using the algebra of functions, specifying domains. Form composite functions. Determine domains for composite functions. Write functions as compositions.

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Finding a Function’s Domain If a function f does not model data or verbal conditions, its domain is the largest set of real numbers for which the value of f(x) is a real number. Exclude from a function’s domain real numbers that cause division by zero and real numbers that result in a square root of a negative number.
Описание слайда:
Finding a Function’s Domain If a function f does not model data or verbal conditions, its domain is the largest set of real numbers for which the value of f(x) is a real number. Exclude from a function’s domain real numbers that cause division by zero and real numbers that result in a square root of a negative number.

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Example: Finding the Domain of a Function Find the domain of the function Because division by 0 is undefined, we must exclude from the domain the values of x that cause the denominator to equal zero. We exclude 7 and – 7 from the domain of g. The domain of g is
Описание слайда:
Example: Finding the Domain of a Function Find the domain of the function Because division by 0 is undefined, we must exclude from the domain the values of x that cause the denominator to equal zero. We exclude 7 and – 7 from the domain of g. The domain of g is

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The Algebra of Functions: Sum, Difference, Product, and Quotient of Functions Let f and g be two functions. The sum f + g, the difference, f – g, the product fg, and the quotient are functions whose domains are the set of all real numbers common to the domains of f and defined as follows: 1. Sum: 2. Difference: 3. Product: 4. Quotient:
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The Algebra of Functions: Sum, Difference, Product, and Quotient of Functions Let f and g be two functions. The sum f + g, the difference, f – g, the product fg, and the quotient are functions whose domains are the set of all real numbers common to the domains of f and defined as follows: 1. Sum: 2. Difference: 3. Product: 4. Quotient:

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Example: Combining Functions Let and Find each of the following: a. b. The domain of The domain of f(x) has no restrictions. The domain of g(x) has no restrictions. The domain of is
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Example: Combining Functions Let and Find each of the following: a. b. The domain of The domain of f(x) has no restrictions. The domain of g(x) has no restrictions. The domain of is

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The Composition of Functions The composition of the function f with g is denoted and is defined by the equation The domain of the composite function is the set of all x such that 1. x is in the domain of g and 2. g(x) is in the domain of f.
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The Composition of Functions The composition of the function f with g is denoted and is defined by the equation The domain of the composite function is the set of all x such that 1. x is in the domain of g and 2. g(x) is in the domain of f.

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Example: Forming Composite Functions Given and find
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Example: Forming Composite Functions Given and find

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Excluding Values from the Domain of The following values must be excluded from the input x: If x is not in the domain of g, it must not be in the domain of Any x for which g(x) is not in the domain of f must not be in the domain of
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Excluding Values from the Domain of The following values must be excluded from the input x: If x is not in the domain of g, it must not be in the domain of Any x for which g(x) is not in the domain of f must not be in the domain of

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Example: Forming a Composite Function and Finding Its Domain Given and Find
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Example: Forming a Composite Function and Finding Its Domain Given and Find

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Example: Forming a Composite Function and Finding Its Domain Given and Find the domain of For g(x), For The domain of is
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Example: Forming a Composite Function and Finding Its Domain Given and Find the domain of For g(x), For The domain of is

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Example: Writing a Function as a Composition Express h(x) as a composition of two functions: If and then
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Example: Writing a Function as a Composition Express h(x) as a composition of two functions: If and then

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