Problem 11
Answer: Not a function
Why not? Because it fails the vertical line test. It is possible to draw a single straight vertical line through more than one point on this blue curve.
Put another way: An input like x = 2 produces more than one output (y = 2 and y = 4 at the same time). If we wanted a function, we need any given input in the domain to produce exactly one and only one output.
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Problem 15
Answers:
- Domain: [tex]-4 \le x \le 2[/tex]
- Range: [tex]2 \le y \le 6[/tex]
Explanation:
The domain is the set of allowed x values. The left-most point on the blue curve is when x = -4, which is the smallest item allowed in the domain. The largest value allowed is x = 2, as this occurs at the right-most point on the blue curve. Therefore, our domain here is [tex]-4 \le x \le 2[/tex]
The range is similar, but we focus on y values this time. The lowest the graph goes is y = 2, and the highest it goes is y = 6. So [tex]2 \le y \le 6[/tex] represents the range of possible y outputs.
For both the domain and range, both endpoints are included.
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Problem 16
Answers:
- Domain: [tex]2 < x < 7[/tex]
- Range: [tex]1 < y < 6[/tex]
Explanation:
We follow the same idea as before. This time however, we have open holes which means that we do not include the endpoints.
The domain is [tex]2 < x < 7[/tex] since the curve spans from x = 2 to x = 7, excluding both of those x values. The range is [tex]1 < y < 6[/tex] for similar reasoning.
Notice how both problems 15 and 16 are functions because they pass the vertical line test. It is not possible to draw a single vertical line through more than one point on either blue curve.
