October 1, 2025

What Is The Domain And Range Of A Function

Q: Can the domain and range of a function be the same?

Yes. For the simple linear function f(x) = x, the set of all possible inputs (domain) is all real numbers, and the set of all possible outputs (range) is also all real numbers.

Q: What is an example of a function with a restricted domain?

The function f(x) = 1/x has a restricted domain. The input x cannot be 0, because division by zero is undefined. Therefore, the domain is all real numbers except 0.

Q: How do you write domain and range using interval notation?

Interval notation uses parentheses () for exclusive boundaries (the endpoint is not included) and brackets [] for inclusive boundaries (the endpoint is included). For example, (2, 7] represents all numbers greater than 2 and less than or equal to 7.

Q: Does the graph of a function show its domain and range?

Yes. The domain is represented by all the x-values covered by the graph from left to right. The range is represented by all the y-values covered by the graph from bottom to top.

Learn the definitions of domain and range in mathematics. Understand how to identify the set of all possible inputs (domain) and outputs (range) for any given function.

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Defining Domain and Range

In mathematics, the domain of a function is the complete set of all possible input values (the 'x' values) for which the function is defined. The range of a function is the complete set of all possible output values (the 'y' values) that result from using the values in the domain.

Section 2: How to Identify Domain and Range

To find the domain, you identify any restrictions on the input. Common restrictions include not being able to divide by zero or take the square root of a negative number. To find the range, you analyze the function's behavior to determine the set of all possible output values it can produce.

Section 3: A Practical Example

Consider the function f(x) = x². The domain is all real numbers, because you can square any number. This is written in interval notation as (-∞, ∞). The range consists of all non-negative numbers, because the result of squaring any real number is always zero or positive. The range is written as [0, ∞).

Section 4: Why Domain and Range Are Important

Understanding the domain and range is crucial for graphing functions and analyzing their real-world applications. It defines the boundaries of the function's behavior, ensuring mathematical operations are valid and providing a complete picture of its possible values.

Frequently Asked Questions

Can the domain and range of a function be the same?

What is an example of a function with a restricted domain?

How do you write domain and range using interval notation?

Does the graph of a function show its domain and range?