Identify the domain of the function shown in the graph.

Identify the domain of the function shown in the graph.

Definition of the domain and range

The domain is all ???x???-values or inputs of a function and the range is all ???y???-values or outputs of a function.

When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.

Identify the domain of the function shown in the graph.

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Basic Functions with Domain Restrictions

Finding the domain and range by looking at the graph of the function

Identify the domain of the function shown in the graph.

Identify the domain of the function shown in the graph.

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Domain and range of the graph of the parabola

Example

What is the domain and range of the function? Assume the graph does not extend beyond the graph shown.

Let’s start with the domain. Remember that domain is how far the graph goes from left to right.

Start by looking at the farthest to the left this graph goes. The ???x???-value at the farthest left point is at ???x=-2???. Now continue tracing the graph until you get to the point that is the farthest to the right. The ???x???-value at this point is at ???2???. There are no breaks in the graph going from left to right which means it’s continuous from ???-2??? to ???2???.

Domain: ???[-2,2]??? also written as ???-2\leq x\leq 2???

Next, let’s look at the range. Remember that the range is how far the graph goes from down to up.

Look at the furthest point down on the graph or the bottom of the graph. The ???y???-value at this point is ???y=1???. Now look at how far up the graph goes or the top of the graph. This is when ???x=-2??? or ???x=2???, but now we’re finding the range so we need to look at the ???y???-value of this point which is at ???y=5???. There are no breaks in the graph going from top to bottom which means it’s continuous.

Range: ???[1,5]??? also written as ???1\leq y\leq 5???

Let’s try another example of finding domain and range from a graph.

Identify the domain of the function shown in the graph.

Remember that The domain is all the defined x-values, from the left to right side of the graph.

Example

What is the domain and range of the function? Assume the graph does not extend beyond the graph shown.

Let’s start with the domain. The ???x???-value at the farthest left point is at ???x=-1???. Now continue tracing the graph until you get to the point that is the farthest to the right. The ???x???-value at this point is at ???3???. There are no breaks in the graph going from left to right which means it’s continuous from ???-1??? to ???3???.

Domain: ???[-1,3]??? also written as ???-1\leq x\leq 3???

Next, let’s look at the range. Look at the furthest point down on the graph or the bottom of the graph. The ???y???-value at this point is ???y=0???. Now look at how far up the graph goes or the top of the graph. This is when ???x=3???, but now we’re finding the range so we need to look at the ???y???-value of this point which is at ???y=2???. There are no breaks in the graph going from down to up which means it’s continuous.

Range: ???[0,2]??? also written as ???0\leq y\leq 2???

Identify the domain of the function shown in the graph.

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How do you find a functions domain on a graph?

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.

How do you identify the domain of a function?

Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.