Rule of thumb · MathematicsNº 77 / 96

A graph is just the equation, drawn

Every point on the curve of y=f(x) is a coordinate pair that makes the equation true — nothing more mysterious than that.

Why it works

Plotting works by sampling many x-values, computing f(x) for each, and connecting the dots — exactly what this tool does, one pixel column at a time. Breaks in the curve mark real discontinuities, like x=0 for 1/x, not drawing errors.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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