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Problem 9 Medium Difficulty

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.

Answer

Yes, the curve is the graph of a function because it passes the Vertical Line Test. The domain is [-3,2] and the range
is [-3,-2)$\cup[-1,3]$.

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Video Transcript

is this the graph of a function? Well, let's try the vertical line test because we know for a function that every X value can have no more than one y value. And so if we pass a vertical line through at any point, it can only pass through one point, not more than one. So there are many places we could pass a vertical line through, and we see it only going through one point on the graph. And even over here, where we have a closed circle and an open circle, it's only going through one point because the open circle is not technically a point. So, yes, this is a function now. What's the domain and what's the range? Remember, the domain is the set of X values that it goes through. And so if we take a look at our graph, it goes through X values from negative three all the way over to positive, too. So the domain would be the interval from negative 3 to 2. It includes every single one of those numbers along the way. The range would be the set of why values so notice that includes why values from a height of negative. Three Joe Hyde of negative, too. But it doesn't include negative, too, because of the open circle. So we have negative three to negative two, not including it there and then notice we have a little gap. And then we have Y values going from a height of negative one all the way up to what I would estimate to be, Oh, about 2.75 So union negative 1 to 2.75

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