Complete the questions on page 288 (5a, 5b, 5c, 5d, 5e, 5f) for practice in describing the end behaviour of a polynomial function.
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It was mentioned previously that, for all polynomials, the leading term dominates the behaviour of the polynomial. This means that the leading term, more specifically the degree, of a polynomial dictates the shape the graph takes.
The graph produced by an n-degree function can have at most n − 1 turning points. A cubic function may, instead, have an inflection point, depending on its shape.
Knowing the number of turning points, or inflection points, a curve has is used to identify a polynomial as linear, quadratic, or cubic. If you are given the graph of a function, you can count the number of turning points or note if an inflection point occurs. After you have counted, you can determine the smallest degree that the function can be. Conversely, in an equation, the degree indicates the general shape of the curve.