If 𝑓 is a function on 𝑥 where set 𝑥 contains the numbers two, four, seven, and nine and where 𝑓 of two equals nine, 𝑓 of four equals two, 𝑓 of seven equals four, and 𝑓 of nine equals seven. Which of the following statements is true? Option A: 𝑓 equals the ordered pairs two, seven; four, two; seven, nine; and nine, four. Option B: 𝑓 contains the ordered pairs two, two; four, four; seven, seven; nine, nine. Option C: 𝑓 contains the ordered pairs two, nine; four, two; seven, four; and nine, seven. Option D: 𝑓 contains the numbers nine, two, four, and seven. Or option E: 𝑓 contains the ordered pairs two, four; four, seven; seven, nine; and nine, two.
As any function needs to contain a set of ordered pairs, coordinates, or points, we can immediately rule out options D in this case. This leaves us with four possible answers. And to work out which one is the correct one, we need to understand what the notation in the question — 𝑓 of two equals nine, 𝑓 of four equals two, and so on — means. 𝑓 of two equals nine, this means that when the 𝑥-value or the domain is two and we substitute that into the function 𝑓, our answer or 𝑦-value or our range is equal to nine. This means that our first ordered pair is two, nine. In the same way, 𝑓 of four equals two means that our second ordered pair is four, two. Likewise, 𝑓 of seven equals four means that we have a third ordered pair seven, four. And finally, 𝑓 nine equals seven means that our fourth and final ordered pair in this case is nine, seven.
This means that the function 𝑓 in this case has the four ordered pairs or coordinates: two, nine; four, two; seven, four; and nine, seven. So the correct answer was C.