Step by step
The question
Question: what is the greatest value of f on this graph of f?
greatest value of f = ?
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 the highest point
The values of f are the heights.
The greatest value is the highest point.
greatest value of f → the top of the graph
Careful!
The value of f is a height.
We answer with it, not with the x.
Careful: the value is the height, f(x), not the x
The top of the graph is the point (1, −1).
The graph never goes higher.
So the greatest value of f is −1.
It is at x = 1.
greatest value = −1
3 Check
Let's check with the dots.
Their heights are −5, −2, −1, −2 and −5.
None is bigger than −1.
So the answer is right!
heights of the dots: −5, −2, −1, −2, −5 biggest: −1
Let's look back.
First: look at the graph.
Then: find the highest point.
Last: check.
Answer
greatest value = −1