Suppose f(x), g(x), and 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 $\ell^2$?
