In the Warm-up we scaled (or stretched) a function \(f(x)\) so that \[ \int_{-1}^{2} a\,f(x) \, dx = 1. \]

Which of the following functions could we scale to satisfy this condition and what is the value of \(a\) in each case?

Which ones lead to problems and why?

How would your answers be different if we changed the condition to \[ \textit{an area of }\,1 \textit{ is enclosed by the curve }y=a\,f(x) \textit{, the }x\textit{-axis and the lines }x=-1\textit{ and }x=2\text{ ?} \]

Can you think of some other functions which cannot be scaled to satisfy one or both of our conditions?