Question Video: Finding the Domain of a Function from Its Graph Mathematics

The figure below shows the graph of a function ๐‘“. What is the domain of the function?

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Video Transcript

The figure below shows the graph of a function ๐‘“. What is the domain of the function?

In this question, weโ€™re given the graph of a function ๐‘“. And we need to use this graph to determine the domain of this function. And we can start by recalling what we mean by the domain of a function. Itโ€™s the set of all input values for that function. And we need to determine this from its graph. To do this, weโ€™ll start by recalling how we sketch the graph of a function. And weโ€™ll do this by using the graph weโ€™re given in the question. We can see that the point with coordinates four, negative three lies on our graph. Since this point lies on the graph of our function ๐‘“, the ๐‘ฅ-coordinate of this point tells us the input value of our function and the ๐‘ฆ-coordinate tells us the corresponding output of our function. Therefore, ๐‘“ evaluated at four is equal to negative three.

And remember, the domain of a function is the set of all input values for that function. Therefore, since four is an input value to our function, because four is the ๐‘ฅ-coordinate of a point which lies on our curve, four is in the domain of ๐‘“. This gives us an equivalent way of finding the domain of a function from its graph. Itโ€™s the set of all ๐‘ฅ-coordinates of points which lie on its graph. We can then use this to determine the domain of a function from its graph. For example, we can see thereโ€™s a point on our graph with ๐‘ฅ-coordinate one, which tells us that one is in the domain of our function.

Similarly, we can see the point with coordinates two, negative three lies on the graph of our function ๐‘“. Therefore, two is a possible input value to our function, and that means two is in the domain of ๐‘“. And we can see the coordinates of the final point on our graph is three, zero. So three is the final element of the domain of our function ๐‘“. And remember, the domain of a function is a set, so we need to write these as a set. Itโ€™s the set containing one, two, three, and four, the ๐‘ฅ-coordinates of the four points in the graph of ๐‘“. Therefore, we were able to determine the domain of the function given in the graph. Itโ€™s the set containing one, two, three, and four.

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