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A graph is a powerful way to visualize the behavior of a function. To see how, let's start with a super basic example:
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From the diagram above we see that
f(6)=3
f(8)=0
f(−9)=−1
If we call the input of the function x, and name the output y=f(x), then each input-output pair becomes a point:
We can then plot these points on the cartesian plane:
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In summary, the graph of a function shows all the points (input,output), with the x-axis representing the inputs and the y-axis representing the outputs.