Step by step
The question
Question: for which x is f(x) = 0 on this graph of f?
There are four choices.
First we solve it, the normal way.
Then we pick.
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.
2 Find where f(x) = 0
This time we know f(x): it is 0.
We look for the x.
Careful!
Do not stop at the first x.
The graph can have the same height more than once.
Start at 0 on the y axis.
Go across, all the way.
The graph is at that height at x = −1.
It is on the x axis already.
And again at x = 3.
So x = −1 or x = 3.
3 Check
Let's check.
Each answer gives a point.
(−1, 0) means left 1, then stay at 0.
It lands on the graph.
And (3, 0) means right 3, then stay at 0.
It is on the graph too.
So the answer is right!
4 Pick the choice
Our answer is x = −1 or x = 3.
That is choice B.
5 Why not the others
A is −3.
Wrong: that is f(0): where it crosses the y axis.
C is 1.
Wrong: that is the lowest point, where f(x) = −4.
D is −2 and 4.
Wrong: there f(x) = 5, not 0.
Let's look back.
First: look at the graph.
Then: find where f(x) = 0.
Then: check.
Then: pick the choice.
Last: why not the others.