Graphs and Transformations

Recognising the standard curves and transforming them — translations, stretches and reflections of y = f(x).

Knowing the shape of the standard curves, and how they move when you change the equation, lets you sketch almost anything quickly.

The standard curves

Quadratic

y = x^2

— a parabola.

Cubic

y = x^3

— rises through the origin with a point of inflection.

Reciprocal

y = \dfrac{1}{x}

— two branches with the axes as asymptotes.

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