Solve equations of the form f(x)=g(x) approximately by finding graph/table intersections.
Approximate a crossing point from a function-comparison table
Problem
Use the comparison table below. Report an exact intersection row when present; otherwise report an adjacent \(x\)-bracket and the function order at each endpoint.
A table can show an intersection exactly, so we should look for equality before settling for an interval estimate. We’ll compare both output entries in every common-input row. If a row matches, its input and shared output form the intersection point; only when no row matches would we look for adjacent rows where the function order reverses.
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