Step by step
The question
Question: is {(−1, 3), (0, 5), (2, 3), (5, 0)} a function?
{(−1, 3), (0, 5), (2, 3), (5, 0)}
A function is a rule where each x has only one y.
One x in, one y out.
function: each x has only one y
1 Each x and its y
We take each x and see where it goes.
−1 goes to 3.
−1 → 3
0 goes to 5.
0 → 5
2 goes to 3.
2 → 3
5 goes to 0.
5 → 0
Careful!
3 comes out twice, from two different x's.
That is fine.
Only one x with two y's breaks the rule.
Careful: the same y twice is fine (3)
2 Read the answer
Every x has only one y.
So yes, it is a function.
= yes, a function
3 Check
Let's check on a grid.
Draw the grid.
We plot the points.
A straight up-and-down line meets at most one point.
Here at x = −1: one point.
No up-and-down line meets two points.
It is a function.
The same answer!
Let's look back.
First: each x and its y.
Then: read the answer.
Last: check.
Answer
= yes, a function