curve sketching

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When a graph y=f(x) is to be sketched, what is generally required is a sketch showing the general shape of the curve and the behaviour at points of special interest. The different parts of the graph do not have to be to scale. It is normal to investigate the following: symmetry, stationary points, intervals in which the function is always increasing or always decreasing, asymptotes (vertical, horizontal and slant), concavity, points of inflexion, points of intersection with the axes, and the gradient at points of interest.

Subjects: Mathematics.

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