The curve \(y = 3 ^ { x }\) can be transformed to the curve \(y = 3 ^ { x - 2 }\) by a translation. Give details of the translation.
Alternatively, the curve \(y = 3 ^ { x }\) can be transformed to the curve \(y = 3 ^ { x - 2 }\) by a stretch. Give details of the stretch.
Sketch the curve \(y = 3 ^ { x - 2 }\), stating the coordinates of any points of intersection with the axes.
The point \(P\) on the curve \(y = 3 ^ { x - 2 }\) has \(y\)-coordinate equal to 180 . Use logarithms to find the \(x\)-coordinate of \(P\), correct to 3 significant figures.
Use the trapezium rule, with 2 strips each of width 1.5, to find an estimate for \(\int _ { 1 } ^ { 4 } 3 ^ { x - 2 } \mathrm {~d} x\). Give your answer correct to 3 significant figures.