Question

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

Answer 1

Two Answers:

Function h (third choice)

Function k (sixth choice, or last choice)

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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.