Problem 1
Answers:
Domain: [tex]-3 \le x < 5[/tex]
Range: [tex]-4 < y \le 3[/tex]
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Explanation:
The domain is the set of allowed x inputs of a function. The smallest x value we can use is x = -3 (note the very left-most point of the graph). The right-most point involves x = 5, but we can't actually use this x value due to the open hole. So that's why we don't have "or equal to" attached to the 5.
The range is the set of possible y outputs. The lowest we can go is y = -4, but we don't include this as part of the range. The largest y can get is y = 3. So the range is [tex]-4 < y \le 3[/tex]
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Problem 2
Answers:
Domain: [tex]-2 < x < 4[/tex]
Range: [tex]-2 < y < 5[/tex]
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Explanation:
We use the same idea as in problem 1. Both endpoints are open holes, so we don't include them as part of the domain and range. For instance, we can't include x = 4 but we can get closer and closer to it. The same idea applies to the range as well.
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Problem 3
Answers:
Domain: [tex]1 \le x \le 4[/tex]
Range: [tex]-4 \le y \le -1[/tex]
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Explanation:
The same idea applies as used earlier. This time we include both endpoints, so we have "or equal to" as part of each inequality sign.
