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Explanation:
The left-most point on the graph is at (-3, -5) which is a closed circle. So this point is on the graph. The x coordinate here is x = -3. This is the smallest x value we can plug into the function, so it is the smallest value in the domain.
The upper boundary of the domain is x = 3. We can't actually use 3 itself since there is a open hole at the point (3,-5), meaning that this point isn't part of the graph. We can only get closer and closer to x = 3 but not get there.
So we can say the domain is the set of real numbers x such that [tex]-3 \le x < 3[/tex] meaning that x is between -3 and 3, where we include -3 but exclude 3. To write this in interval notation, you would write [-3, 3)
The square bracket means "include this endpoint". The curved parenthesis means "exclude this endpoint.
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The range is handled in a similar fashion. We look at the y values this time. The smallest y coordinate is y = -5, which is from the point (-3, -5). The largest y value is y = 4 at the point (0,4). We can pick any y value between -5 and 4, including both endpoints, so we say
range = set of all y values such that [tex]-5 \le y \le 4[/tex]
which in interval notation translates to [-5, 4]
