$f(x) = x − 2.$
Sketch $y = f(f(f(x)))$
for $x\in \mathbb{R}.$

Why not start by sketching
$f(x)?$

How does changing the argument to
$x$
affect the graph? What would$f(x)$
look like? 
What about
$f(f(x))?$

A good way to think about this graph is to consider the sequence of transformations we are performing. Applying
$\cdot$
to the argument of the function makes it symmetrical about the yaxis. Subtracting$2$
shifts the entire graph downwards by$2$
units and applying$\cdot$
to the result flips parts of the graph below the xaxis. By sketching the simpler cases, we can deduce the pattern that$n$
applications of$f$
results in$n$
peaks.