Every point on the curve of y=f(x) is a coordinate pair that makes the equation true — nothing more mysterious than that.
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.
Until the drawing lies. A curve sampled too coarsely can miss a spike entirely, a log axis makes exponential growth look linear, and a truncated y-axis makes a 2% change look like a collapse. The equation is true; the picture of it is a set of choices.
Estimate with the rule, then check it against the calculator that models it properly.
Open Graphing Calculator →