### Video Transcript

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

In this question, weโre 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. Itโs the set of all input values for that function. And we need to determine this from its graph. To do this, weโll start by recalling how we sketch the graph of a function. And weโll do this by using the graph weโre 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 ๐ฅ-coordinate of this point tells us the input value of our function and the ๐ฆ-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 ๐ฅ-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. Itโs the set of all ๐ฅ-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 thereโs a point on our graph with ๐ฅ-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. Itโs the set containing one, two, three, and four, the ๐ฅ-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. Itโs the set containing one, two, three, and four.