Suppose \(f(x), g(x), h(x)\) are all linear functions, and \(j(x) \) and \(k(x)\)are defined by
\(j(x) = \max\{f(x),g(x),h(x)\} \)
\(k(x) = \min\{f(x),g(x),h(x)\}.\)
This means that, for each \(x\), we define \(j(x)\)to be equal to either \(f(x), g(x), or, h(x)\) whichever is greatest; similarly, \(k(x)\) is the least of these three values.
Shown below is the graph of \(y=j(x)\) for \(-3.5\le x\le 3.5\).
Let \(\ell\) be the length of the graph of \(y=k(x) for -3.5\le x\le 3.5\). What is the value of \(\ell^2\)?
