4.06: Modulus graph and function

Sketch \(y=|x^2-5|\), stating the intercepts with the coordinate axes.

\(f(x)=ax+b\), where \(a\) and \(b\) are non-zero integers. The solutions of \(|f(x)|=4\) are \(x=2.5\) and \(x=-1.5\). Find the possible functions \(f\).