The vertical displacement hhh (in decimetres) of an industrial piston at time ttt (where t∈Rt \in \mathbb{R}t∈R) is modelled by the cubic function:
h(t)=t(t−12)(t−k) h(t) = t(t - 12)(t - k) h(t)=t(t−12)(t−k)where kkk is a constant such that k>12k > 12k>12.
Sketch the graph of y=h(t)y = h(t)y=h(t) on a set of axes, labelling the coordinates of the points where the graph intersects the ttt-axis.
After a mechanical recalibration, the displacement is modelled by the transformed function g(t)=h(10−2t)g(t) = h(10 - 2t)g(t)=h(10−2t). Sketch the graph of y=g(t)y = g(t)y=g(t) on separate axes, labelling the coordinates of the points where the graph intersects the ttt-axis in terms of kkk.
