Graphing techniques

Check the graph and its symmetries · Diagrams

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Reflection axes: five basic curves

Test reflection symmetry

Choose a curve and a mirror line, then move point P.

Curve

Mirror line

Point input x1.5

P = (1.5, 2.25)P′ = (-1.5, 2.25)The reflected point lies on the curve.

A matching point is not a proof of symmetry.

Why this works

The y-axis, x = 0, is a reflection axis.

A matching point alone does not prove reflection symmetry. Compare the whole curve; the overlay is clipped to the viewing window. Solid and dashed lines identify the original and reflected curves.

Five source rows: upward parabola y=x² symmetric in x=0; sideways parabola x=y² in y=0; absolute-value V in x=0; reciprocal branches in y=x and y=−x; cosine with amplitudes ±1 and displayed axis x=0. Full cosine also has axes x=kπ.

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