Find the coordinates of the points 𝑓 of two, 𝑓 of 17, and 𝑓 of 31 given 𝑓 of 𝑥 is equal to 𝑥 plus 12.
So here we have this function: 𝑓 of 𝑥 equals 𝑥 plus 12. And we are asked to find coordinates of the points. Well, a coordinate is 𝑥 comma 𝑦. So notice, for 𝑓 of 𝑥, all of these numbers — two, 17, 31 — these are the 𝑥s. And when we plug these numbers into the function, it will give us the answer which is the 𝑦-coordinate. So we plug in our 𝑥 here. And 𝑓 of 𝑥 will actually be our answer for 𝑦.
So let’s begin with 𝑓 of two. So instead of 𝑥 plus 12, we plug in two for 𝑥. So two plus 12 gives us 14. So again, when we plugged in two, we got an answer of 14. So two is 𝑥 and 14 is 𝑦. That would be our coordinate.
Now for 17, we plugged that in for 𝑥. And now, we take 17 plus 12 which is 29. So when we plugged in 17, we got 29. So our coordinate would be 17, 29. Lastly, we plug in 31 in for 𝑥. And 31 plus 12 is 43. So 31, 43 will be our coordinate. Therefore, the coordinates two, 14; 17, 29; and 31, 43 will be the coordinates of these points.