Worked examples
The question
Question: is {(1, 2), (2, 4), (3, 6)} a function?
{(1, 2), (2, 4), (3, 6)}
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 2.
1 → 2
2 goes to 4.
2 → 4
3 goes to 6.
3 → 6
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.
▶ Watch it solved
The question
Question: is y = |x| a function?
y = |x|
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 Draw the graph
Draw the grid.
Draw y = |x|.
It is a V shape.
2 Vertical line test
The vertical line test: draw straight up-and-down lines.
If one of them hits the graph two times, one x has two y's.
Then it is not a function.
Here is a vertical line at x = 2.
It hits the graph only once.
Any other vertical line also hits it only once.
every vertical line: 1 hit → a function
3 Read the answer
No vertical line hits it two times.
So yes, it is a function.
= yes, a function
4 Check
Let's check with numbers.
x = 2 gives y = 2.
Only one y.
The same answer!
x = 2: y = |2| = 2 (one y)
Let's look back.
First: draw the graph.
Then: vertical line test.
Then: read the answer.
Last: check.
▶ Watch it solved
The question
Question: is {(0, 0), (1, 1), (1, −1), (4, 2)} a function?
{(0, 0), (1, 1), (1, −1), (4, 2)}
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 0.
0 → 0
1 goes to 1 and −1.
One x, two different y's!
1 → 1, −1
4 goes to 2.
4 → 2
2 Read the answer
1 has two y's.
So it is not a function.
= no, not a function
3 Check
Let's check on a grid.
Draw the grid.
We plot the points.
A straight up-and-down line at x = 1 meets two points.
Two points on one up-and-down line: not a function.
The same answer!
Let's look back.
First: each x and its y.
Then: read the answer.
Last: check.
Answer = no, not a function
▶ Watch it solved
