Lesson 82 -- Evaluating Functions -- Domain and Range. Example 82.1. Example 82.2. Example 82.3. Domain and Range.
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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.
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.
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,
y = 4 here
y = 0 here
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,
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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