negative 4 up to 5. Now some students think that we should

not include 5 in our range because of this open circle over here.

However if you look over here. There is a point on the graph with the Y

coordinate equal to 5, which is why we include 5 here.

Therefore these would be our answers here.

All right, let's look at another example. [SOUND] Here's the graph of G.

Let's find its domain and range. Again the graph is the set of all ordered

pairs x, y such that y is equal to g of x, and again the domain is this set of

all possible x coordinates of points on the graph, and the range is the set of

all y coordinates of points in the graph. Okay, so what is the domain? What is the

set of all possible X coordinates of points on our graph? [SOUND] So here's

our graph. Again, think of projecting the graph on

to the x axis. So the domain then would be this interval

here, together with this interval here. That is the domain equal to negative 2 to

negative 1 union 0 up to 4. Notice a few things here.

Again, because of this open circle here, this is open.

x=4 is not the x coordinate of any point in our graph.

And also, notice here there's this gap between negative 1 and 0 because those x

values are not the x coordinate of any point on our graph.

Neither are the x values to the right of 4 or the x values to the left of negative

2. So this is our domain.

Now what about the range? [SOUND] Again, looking at our graph, remember the range

is the set of all possible y coordinates of points on our graph.

Again, thinking of projecting this graph onto the y-axis will give us this

interval here. That is the range is equal to the

interval from 1 to 5. And we're not including 5 here, because 5

is not the y coordinate of any point on our graph.

Now, sometimes students get confused, and they won't include this bottom portion

here. Because they're only looking at this

piece of the graph. But aren't these Y values here Y

coordinates for points over here? So they are Y coordinates for points on

our graph. So we include the entire interval from 1

up to 5. So this is our range here,

and this is how we find the domain and range of a function, given it's graph.

Thank you, and we'll see you next time.

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