HOMEWORK 13
RICKY NG
Question 13.1. Does this graph represent a function?
Solution. Pass the vertical line test, so it’s a function.
Question 13.2. Does this graph represent a function?
Solution. Does not pass the vertical line test (the line x = 0), so it is a not function. Question 13.3. Does this graph represent a function?
Solution. Pass the vertical line test, so it is a function.
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Question 13.4. Does this graph represent a function?
Solution. Does not pass the vertical line test (the vertical line), so it is not a function. Question 13.5. Determine whether or not the set of points represents a function. Justify your answer.
{(−3, 2), (1, 2), (0, −3), (2, 1), (−2, 1)}
Solution. Look at the x-coordinates of these points, they are all distinct. This means
that every number in X is precisely assigned once to some number in Y , so it represents
a function.
Question 13.6. Find the domain of the following graph:
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Solution. Notice that the solid dot on the left means we start at x = −3 inclusively,
and the empty dot on the right means we end at x = 6, exclusively. Every number in
[−3, 6) has an assigned value by g, so the domain is [−3, 6).
Question 13.7. Find the range of the graph above.
Solution. Let’s look for the largest and least y-values the graph reaches. It is least at
x = −3, and g(−3) = −2. Similarly, it is largest at x = 3 where g(3) = 7. Since g is
continuous, its range is [−2, 7].
Question 13.8. From the graph above, find g(−2)
Solution. From the graph above, g(−2) = 0. (Look for x = −2 on x-axis and look up
until we hit the graph.)
Question 13.9. From the graph above, find g(1)
Solution. From the graph above, g(1) = 3. (Look for x = −1 on x-axis and look up until
we hit the graph.)
Question 13.10. From the graph above, for what value(s) of x is g(x) = −2?
Solution. Look for y = −2 on the y-axis, and move across horizontally. Then capture all
the x’s at which we hit the graph. In this case, we only have x = −3.
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