Analyzing Graphs of Absolute Value Functions

An absolute value function is any function that contains the absolute value of an expression. In other words, any function that can be described as a transformation of the function $f(x)=|x|.$ Since the absolute value of an expression is never negative, the graph of the function $f(x)=|x|$ will always lie on or above the $x$-axis. Note that $|\text{-} 5| = 5 \quad \text{and} \quad |5|=5.$ This means, the points $(\text{-} 5,5)$ and $(5,5)$ both lie on $f(x)=|x|.$ As it turns out, these points lie directly across from each other. In fact, this symmetry exists for all inverse input values. Thus, absolute value graphs have a distinct V-shape.