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What Is a Domain of a Function OR

# What Is a Domain of a Function

This piece of content will help you understand what a domain of a function is and the benefits. It will also help you identify the domain of a function for a given function.

### Domain

via GIPHY

If a real function f is given by a formula, it may be not defined for some values of the variable. In this case, it is a partial function, and the set of real numbers on which the formula can be evaluated to a real number is called the natural domain or domain of definition of f. In many contexts, a partial function is called simply a function, and its natural domain is called simply its domain.

The domain of a function is the set of input values, [latex]x[/latex], for which a function is defined. The domain is shown in the left oval in the picture below. The function provides an output value, [latex]f(x)[/latex], for each member of the domain. The set of values the function outputs is termed the range of the function, and those values are shown in the right hand oval in the picture below. A function is the relation that takes the inputs of the domain and output the values in the range. The rule for a function is that for each input there is exactly one output. (Source: courses.lumenlearning.com)

### Value

We can also tell this mapping, and set of ordered pairs is a function based on the graph of the ordered pairs because the points do not make a vertical line. If an [latex]x[/latex]value were to repeat there would be two points making a graph of a vertical line, which would not be a function. Let’s look at this mapping and list of ordered pairs graphed on a Cartesian Plane.

In order to find the domain of a function, if it isn’t stated to begin with, we need to look at the function definition to determine what values are not allowed. For instance, we know that you cannot take the square root of a negative number, and you cannot divide by [latex]0[/latex]. With this knowledge in hand, let’s find the domain of a function. (Source: courses.lumenlearning.com)

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