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June 2025 p12 q1
4096
The diagram shows the graphs with equations \(y = f(x)\) and \(y = g(x)\).
Describe fully a sequence of two transformations which transforms the graph of \(y = f(x)\) to the graph of \(y = g(x)\). Make clear the order in which the transformations should be applied.
Solution
1. Apply a vertical stretch by a factor of 2. This transformation changes the graph of \(y = f(x)\) to \(y = 2f(x)\), effectively doubling the y-values of all points on the graph.
2. Translate the graph vertically by \(\begin{pmatrix} 0 \\ -14 \end{pmatrix}\). This moves the graph down by 14 units, resulting in the graph of \(y = g(x)\).