Power function

Learning objectives

To identify the graph of the power function (y = axⁿ) by the nature of its exponent n (whole, positive, negative, rational) and the coefficient a.
To study the domains, limits and asymptotes of the functions y = axⁿ, y = ax^1/n, and y = ax^-n.
To introduce the vocabulary associated with each function.

A power function is defined by the general expression f(x)=axⁿ where the exponent n can be a whole or a real number (positive or negative). The coefficient a is a real number.

This simulation allows us to see the influence of the parameters a and n on the shape of the curve f(x) and study the following characteristics:

the scale factor,
the limits at infinity or the point of divergence,
the domain,
the asymptotes,

Change the settings a and n to analyze characteristics of some functions such as the quadratic, cube, inverse, or root functions… recognize their characteristic shapes such as the parabola or hyperbole.