I am supposed to express the following function as a linear combination of step function: $\left | \varphi \right |,\varphi ^{3},\varphi -\gamma , max\left \{ \varphi ,\gamma \right \}$, where:
$$\varphi\left ( x \right )=\left\{\begin{matrix} 3 & -2\leq x\leq 2 & \\ -1 & 0< x< 4 & \\ 1 & 4\leq x< 5 & \end{matrix}\right.$$
$$\gamma\left ( x \right )=\left\{\begin{matrix} 1 & 0\leq x\leq 1\\ 1 & 2\leq x\leq 5 \end{matrix}\right.$$
I know, how to draw them separately, but I do not understand, how I am supposed to make the linear combination.
Can anyone help me?