A-level · Algebra & functions

Transformations of graphsExam-style questions

Moving, stretching and reflecting a graph by changing its equation. Why a change outside the bracket acts on y as written; why a change inside acts on x and works backwards; stretches parallel to the x-axis and their scale factor; the two reflections; tracking a point through a combined transformation; and writing the equation of a transformed curve.

Start practising Read the lesson

13 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows the curve $y = f(x)$ , which has a maximum point at $(-2, 5)$ and crosses the $x$ -axis at $(-5, 0)$ and $(1, 0)$ .On separate diagrams, sketch
(a) $y = f(-x)$ and (b) $y = 2f(x)$ . In each case give the coordinates of the new maximum point and of the points where the curve crosses the $x$ -axis.
Level 5 · 4 marksTry it
2
The curve $y = f(x)$ has a minimum point at $(1, -2)$ . The curve is transformed to $y = -f(x - 3)$ . Describe the two transformations involved, and state the coordinates of the turning point of the new curve, stating whether it is a maximum or a minimum.
Level 5 · 3 marksTry it