Lesson 82 -- Evaluating Functions -- Domain and Range

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# Lesson 82 -- Evaluating Functions -- Domain and Range - PowerPoint PPT Presentation

Lesson 82 -- Evaluating Functions -- Domain and Range. Example 82.1. Example 82.2. Example 82.3. Domain and Range.

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Domain and Range

In this class, we will use only the real numbers as replacements for x and we accept only values for f(x) that are real numbers. Therefore,we cannot use numbers as replacements for x that result in division by zero or that require us to take the square roots of negative numbers.

Definition of a Function

A function is a mapping from one set called the domain to another set called the range such that

1. Each element of the domain is mapped to precisely one element of the range, and

2. Each element of the range corresponds to at least one member of the domain.

Example 82.4

f

We can use any real number value for x, so the domain of f is the set of real numbers. We can write this as:

The range of f is all those values that f(x) can assume. It turns out that the range of f is also the set of real numbers, as is apparent from the graph of f.

Example 82.5

We see that the function f can be applied to any real number, so

The only value the function ever attains is 3. No matter if x = 0 or x = 1,000,000, f(x) = 3. Therefore,

Example 82.6

4

y = 4 here

0

y = 0 here

-2

3

Example 82.7

Remember we said earlier,we cannot use numbers as replacements for x that result in division by zeroor that require us to take the square roots of negative numbers. Therefore,

Example 82.8

Remember we said earlier,we cannot use numbers as replacements for x that result in division by zero or that require us to take the square roots of negative numbers.Therefore,

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