Power function: definition, formula, types of graphs

In this publication, we will consider the definition and formula of a power function, and also show the possible types of its graphs (straight line, hyperbola, parabola, etc.).

Content

Power function definition

Power function is a function of the form f (x) = x a, where:

  • a – exponent, is a real number, a ≠ 0;
  • x – the base of the degree, this is a free variable.

examples:

  • y=x 2
  • y=x 3
  • y=x 0,5

A power function is often referred to as a function of the form y=kx aWhere k is any non-zero coefficient.

Power function graph

The type of graph depends on what values ​​the exponent takes. a and coefficient k function.


коэффициент» data-order=»Показатель

степени и

коэффициент» style=»min-width:21.0351%; width:21.0351%;»>Показатель

степени и

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k > 0″ data-order=»a < 0 (четное целое число), k > 0″>a < 0
(четное целое число),

k > 0


k < 0″ data-order=»a < 0 (четное целое число), k < 0″>a < 0
(четное целое число),

k < 0


k > 0″ data-order=»a < 0 (нечетное целое число), k > 0″>a < 0
(нечетное целое число),

k > 0


k < 0″ data-order=»a < 0 (нечетное целое число), k < 0″>a < 0
(нечетное целое число),

k < 0


k > 0″ data-order=»0 < a < 1, (дробное число), k > 0″>0 < a < 1,
(дробное число),

k > 0


k < 0″ data-order=»0 < a < 1 (дробное число), k < 0″>0 < a < 1
(дробное число),

k < 0


k > 0″ data-order=»a < 0 (дробное число), k > 0″>a < 0
(дробное число),

k > 0


k < 0″ data-order=»a < 0 (дробное число), k < 0″>a < 0
(дробное число),

k < 0

Function graph
a = 1, k < 0«>Power function: definition, formula, types of graphsPower function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs
«>Power function: definition, formula, types of graphs

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