This week in Precalculus 11, we started the Absolute Value and Reciprocal Functions unit. We first learned about absolute value functions.
Absolute value function: y = |f(x)|
Critical points: an absolute value function’s x-intercepts
An absolute value function’s graph changes direction at the critical points. To graph an absolute value function, we first graph its equivalent normal function [y = f(x)]. Any points below the x-axis are reflected along the x-axis, since absolute values are only positive.
An absolute value function can be written in piecewise notation. To do so, we write one function in which the absolute value expression is positive or 0, and one function in which the absolute value expression is negative. We then state when this occurs, using </>/≥/≤ and the critical point.