Michigan Algebra I Sept. 2012

Recall from the previous lesson, that the family of functions known as the power functions take the form, y = kx^p. The shape of the graph of these power functions depends on the sign of k and the value of p. The coefficient k will change the scale of the graph and, if negative, flip the graph across the x-axis.

All graphs of y = x^p pass through the point (1,1). Beyond that, the shape and growth for large positive x is given by:

· p >1: resembles a quadratic when even or a cubic when odd. Grows as x grows larger. Example: y = x²

· p = 1: the line y = x. Grows as x grows larger. Example: y = x

· 0 < p <1: concave down. Grows as x grows larger. Example: y = x^(½)

· p = 0: the line y = 1. Example:y = x⁰ = 1