Definition:Secant Line

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Let $f: \R \to \R$ be a real function.

Let the graph of $f$ be depicted on a Cartesian plane.


A secant to $f$ is a straight line which intersects the graph of $f$ in (at least) two points.

In the above diagram, the secant is the line $AB$ in $\color {blue} {\text {blue} }$.

Linguistic Note

The word secant comes from the Latin secantus (that which is cutting), the present participle of secare to cut.

This arises from the fact that it is the length of the line from the origin which cuts the tangent line.

It is pronounced with the emphasis on the first syllable and a long e: see-kant.