Question Video: Expressing a Function Using a Set of Ordered Pairs | Nagwa Question Video: Expressing a Function Using a Set of Ordered Pairs | Nagwa

Question Video: Expressing a Function Using a Set of Ordered Pairs

If 𝑓 is a function on 𝑋, where 𝑋 = {2, 4, 7, 9}, 𝑓(2) = 9, 𝑓(4) = 2, 𝑓(7) = 4, and 𝑓(9) = 7, which of the following sets of ordered pairs represents 𝑓? [A] {(2, 9), (4, 2), (7, 4), (9, 7)} [B] {(2, 4), (4, 7), (7, 9), (9, 2)} [C] {9, 2, 4, 7} [D] {(2, 2), (4, 4), (7, 7), (9, 9)} [E] {(2, 7), (4, 2), (7, 9), (9, 4)}

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Video Transcript

If 𝑓 is a function on 𝑋, where 𝑋 is the set of numbers two, four, seven, nine; 𝑓 of two is equal to nine; 𝑓 of four is equal to two; 𝑓 of seven is equal to four; and 𝑓 of nine is equal to seven, which of the following sets of ordered pairs represents 𝑓? Is it (A) the set of ordered pairs two, nine; four, two; seven, four; and nine, seven? (B) The set of ordered pairs two, four; four, seven; seven, nine; and nine, two. (C) The set of numbers nine, two, four, and seven. (D) The set of ordered pairs two, two; four, four; seven, seven; and nine, nine. Or (E) the set of ordered pairs two, seven; four, two; seven, nine; nine, four.

In this question, we are told that 𝑓 is a function on 𝑋, where 𝑋 contains the values two, four, seven, and nine. We are then given the values of 𝑓 of two, 𝑓 of four, 𝑓 of seven, and 𝑓 of nine and are asked to identify the sets of ordered pairs that represents 𝑓.

We can immediately rule out option (C) as this is just a set of four numbers. It is actually the set of 𝑦 numbers: the values of 𝑓 of two, 𝑓 of four, 𝑓 of seven, and 𝑓 of nine, as these are nine, two, four, and seven, respectively.

We recall that a function takes every member of a set and maps it onto exactly one member in a second set. When we’re considering ordered pairs representing a function, we know that the first value is the input value and the second value is the output value.

Our first ordered pair is therefore two, nine, as an input of two gives an output of nine in our function 𝑓. Next, we see that an input of four gives an output of two, so our second ordered pair is four, two. Thirdly, we have the ordered pair seven, four and finally the ordered pair nine, seven. An input of nine gives an output of seven.

This satisfies our definition of a function, as every member of set 𝑋 is mapped onto exactly one member of a second set, where this second set 𝑦 contains the values nine, two, four, and seven. We are looking for the option that matches our four ordered pairs, and this is option (A). The set of ordered pairs that represents the function 𝑓 is two, nine; four, two; seven, four; and nine, seven.

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