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.
