Question

Which sets of points represent one-to-one functions?

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f = {(1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,8)}
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g = {(1,2), (3,3), (5,4), (7,4), (9,4), (11,4), (13,4), (17,4)}
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h = {(1,6), (2,3), (3,16), (4,21), (5,27), (6,36), (7,48), (8,56)}
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i = {(0,1), (1,3), (3,5), (5,3), (7,4), (9,6), (11,9), (13,10)}
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j = {(2,6), (4,16), (6,26), (8,36), (10,16), (12,56), (14,66), (16,16)}
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k = {(2,6), (4,16), (6,26), (8,36), (10,46), (12,56), (14,66), (16,76)}

Answer 1

H = {(1,6), (2,3), (3,16), (4,21), (5,27), (6,36), (7,48), (8,56)}

K = {(2,6), (4,16), (6,26), (8,36), (10,46), (12,56), (14,66), (16,76)}

explanation: PLATO/EDMENTUM

Answer 2

Two Answers:

Function h (third choice)

Function k (sixth choice, or last choice)

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Step-by-step explanation:

A function is only possible if the x values do not repeat. A relation is considered one-to-one only if the y values do not repeat. We combine the two ideas. If we want a one-to-one function, then neither x nor y can repeat.

• Function f has y = 8 repeating, so it is not one-to-one
• Function g is a similar story but y = 4 repeats.
• Function h has all unique x values, and all unique y values. This function is one-to-one.
• Function i has y = 3 repeating, so it is not one-to-one.
• Function j has y = 16 show up more than once, so it is not one-to-one.
• Function k has all unique x values, and all unique y values. This function is one-to-one.

Note: if we had two points like (1,2) and (3,1), then it is still one-to-one (even though the digit 1 shows up twice). This is because the set of x values {1,3} is unique, and so is the set of y values {2,1}. We look at each set separately and not combine the two sets.