# Domain and range of a graph functional relationship

### How to find domain and range from a graph (video) | Khan Academy

Identify the domain and range for relations described with words, symbols, tables, sets of ordered pairs, and graphs. The range of a function or relation is the set of all possible dependent values the relation can produce from the domain. Graphing Relations, Domain, and Range. GRE Resources. Graphing all relations are functions. A function states that given an x, we get one and only one y. A(2)(A) determine the domain and range of a linear function in mathematical problems; Given a verbal statement or a graph of a linear function, determine its domain and range. . Match the Relationship with the Correct Domain and Range.

In most cases, a graph will help show the domain. This is the equation of a straight line.

There are no "problem" spots with this straight line. If a fractional expression contains a variable in its denominator, you need to check for division by zero. The value under the radical needs to be 0 or a positive number no negatives.

It may be necessary to restrict a domain to ensure the existence of a function. We know not all graphs are functions. As we saw in Example 5, it is often possible, however, to create "functions" from non-function graphs by restricting which domain elements are used.

The graph at the left is. At first glance, it appears that this graph passes the Vertical Line Test and is a "function". But it is NOT a function over the domain of Real numbers. If we restrict the domain to be "all Real numbers excluding 2", our relation can be called a function.

Domain of the function: It may be necessary to restrict the range to ensure the existence of a function. The graph of the relation is shown below on the left. We can, however, separate this graph into its two parts and create two separate functions. These separated graphs each pass the Vertical Line Test and are functions. If a domain is not stated, it is generally assumed to be all real numbers. Well, we go up here.

We don't see it's graphed here.

### Domain and range from graph (practice) | Khan Academy

It's not defined for any of these values. It only starts getting defined at x equals negative 6. At x equals negative 6, f of x is equal to 5.

And then it keeps getting defined. When x equals 7, f of x is equal to 5.

### Graphing Relations, Domain, and Range

You can take any x value between negative 6, including negative 6, and positive 7, including positive 7, and you just have to see-- you just have to move up above that number, wherever you are, to find out what the value of the function is at that point. So the domain of this function definition? Well, f of x is defined for any x that is greater than or equal to negative 6.

Or we could say negative 6 is less than or equal to x, which is less than or equal to 7. If x satisfies this condition right over here, the function is defined. So that's its domain.

## Worked example: domain and range from graph

So let's check our answer. Let's do a few more of these. Introduction Relations and functions describe the interaction between linked variables.

These relationships include independent values and inputswhich are the variables that can be manipulated by circumstances. They also include dependent values and outputswhich 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. The domain of a function or relation is the set of all possible independent values the relation can take. It is the collection of all possible inputs. The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.

It is the collection of all possible outputs.