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

Сентябрь 14, 2022

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

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2. Find the domain of a function. Combine functions using the algebra of functions, specifying domains. Form
3. Finding a Function’s Domain If a function f does not model data or verbal conditions, its
4. Example: Finding the Domain of a Function Find the domain of the function Because division by
5. The Algebra of Functions: Sum, Difference, Product, and Quotient of Functions Let f and g be
6. Example: Combining Functions Let and Find each of the following: a. b. The domain of The
7. The Composition of Functions The composition of the function f with g is denoted and is
8. Example: Forming Composite Functions Given and find
9. Excluding Values from the Domain of The following values must be excluded from the input x:
10. Example: Forming a Composite Function and Finding Its Domain Given and Find
11. Example: Forming a Composite Function and Finding Its Domain Given and Find the domain of For
13. Скачать презентацию

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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.

Objectives:

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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.

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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

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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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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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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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