Step by step
The question
Question: is {(0, 1), (1, 1), (2, 1)} a function?
{(0, 1), (1, 1), (2, 1)}
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.
0 goes to 1.
0 → 1
1 goes to 1.
1 → 1
2 goes to 1.
2 → 1
Careful!
1 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 (1)
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 = 0: 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