# Domain and range definition math

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## Functions: Domain and Range Domain and Range of a Function. Definitions of Domain and Range. Domain. The domain of a function is the complete set of possible values of.

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Easy to understand math lessons on DVD. Try before you commit. The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible x -values which will make the function "work", and will output real y -values. This will make the number under the square root positive.

Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions such as these. In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions.

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All of the values that can go into a relation or function input are called the domain. All of the values that come out of a relation or function output are called the range. Range may also be referred to as "image". Note that both relations and functions have domains and ranges. The domain is the set of all first elements of ordered pairs x -coordinates. The range is the set of all second elements of ordered pairs y -coordinates. Only the elements "used" by the relation or function constitute the range.

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis. The range is the set of possible output values, which are shown on the y -axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values. See Figure 6. Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range. Figure 9.

Functions v. When functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. These won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. Domain and Range. The above list of points, being a relationship between certain x 's and certain y 's, is a relation.

## Domain and Range of a Function

Domain and Range. Learning Objective s. Relations and functions describe the interaction between linked variables. These relationships include independent values and inputs , which are the variables that can be manipulated by circumstances. They also include dependent values and outputs , which are the variables that are determined by the independent values. There is another pair of components we must consider when talking about relations, called domain and range.

In its simplest form the domain is all the values that go into a function, and the range is all the values that come out. Please read " What is a Function? Example: this tree grows 20 cm every year, so the height of the tree is related to its age using the function h :. Now, what comes out the Range depends on what we put in the Domain In fact the Domain is an essential part of the function. Change the Domain and we have a different function. Even though both functions take the input and square it, they have a different set of inputs , and so give a different set of outputs.

## Domain and Range

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math Algebra I Functions Introduction to the domain and range of a function. Intervals and interval notation. What is the domain of a function?

The domain of a function f x is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. In grammar school, you probably called the domain the replacement set and the range the solution set. They may also have been called the input and output of the function. D is not in the domain, since the function is not defined for D. You can also talk about the domain of a relation , where one element in the domain may get mapped to more than one element in the range. Here, the relation is given as a set of ordered pairs. Note that the domain elements 1 and 2 are associated with more than one range elements, so this is not a function.

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## 5 thoughts on “Domain and range definition math”

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Functions: Domain and Range | Purplemath

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Input and Output

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Finding the Domain of a Function Defined by an Equation

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Domain and Range - Mathematics LibreTexts