Worked examples
The question
Question: find f(2) on this graph of f.
f(2) = ?
1 Look at the graph
The graph shows f.
x goes across.
The height of the graph is f(x): we read it on the y axis.
x: across
f(x): the height, up
2 Read f(2)
The number in the brackets is the x.
Here x is 2.
f(2): x = 2 → f(x) = ?
Careful!
f of 2 does not mean a height of 2.
The 2 in the brackets is an x.
So we start at 2 on the x axis.
Careful: f(2): start at x = 2, not at a height of 2
So f(2) = 3.
f(2) = 3
3 Check
Let's check.
The answer gives a point.
(2, 3) means right 2, then up 3.
It lands on the graph.
So the answer is right!
(2, 3): right 2, up 3 → on the graph
Let's look back.
First: look at the graph.
Then: read f(2).
Last: check.
▶ Watch it solved
The question
Question: for which x is f(x) = 3 on this graph of f?
f(x) = 3 x = ?
1 Look at the graph
The graph shows f.
x goes across.
The height of the graph is f(x): we read it on the y axis.
x: across
f(x): the height, up
2 Find where f(x) = 3
This time we know f(x): it is 3.
We look for the x.
f(x) = 3 → height 3 → x = ?
Careful!
Do not stop at the first x.
The graph can have the same height more than once.
Careful: look for every x: f(x) can be 3 more than once
So x = 0 or x = 2.
x = 0 or x = 2
3 Check
Let's check.
Each answer gives a point.
(0, 3) means stay at 0, then up 3.
It lands on the graph.
(0, 3): stay at 0, up 3 → on the graph
And (2, 3) means right 2, then up 3.
It is on the graph too.
So the answer is right!
(2, 3): right 2, up 3 → on the graph
Let's look back.
First: look at the graph.
Then: find where f(x) = 3.
Last: check.
▶ Watch it solved
The question
Question: for which x is f(x) = −3 on this graph of f?
f(x) = −3 x = ?
1 Look at the graph
The graph shows f.
x goes across.
The height of the graph is f(x): we read it on the y axis.
x: across
f(x): the height, up
2 Find where f(x) = −3
This time we know f(x): it is −3.
We look for the x.
f(x) = −3 → height −3 → x = ?
Careful!
Do not stop at the first x.
The graph can have the same height more than once.
Careful: look for every x: f(x) can be −3 more than once
So x = −1 or x = 1.
x = −1 or x = 1
3 Check
Let's check.
Each answer gives a point.
(−1, −3) means left 1, then down 3.
It lands on the graph.
(−1, −3): left 1, down 3 → on the graph
And (1, −3) means right 1, then down 3.
It is on the graph too.
So the answer is right!
(1, −3): right 1, down 3 → on the graph
Let's look back.
First: look at the graph.
Then: find where f(x) = −3.
Last: check.
▶ Watch it solved
