Graph the points and use the shape to think about what kind of a function f(x) is.
f(x)=x^2-1
Practice makes perfect
From the diagram, we can identify the inputs and outputs of the function.
x
f(x)
10
99
2
3
-3
8
0
-1
Let's plot these points in a coordinate plane and start sketching the graph.
When we look at the graph, we can see that they follow a slightly curved path. This means the function is not a linear function. It could, however, be a quadratic function. If we examine the output we see that they are all 1 below a perfect square.
x
x^2
=
x^2-1
10
10^2
100
99
2
2^2
4
3
-2
( -3)^2
9
8
0
0^2
0
-1
Therefore, the function can be written in the following way.
f(x)=x^2-1
