IB Maths AA HL Sl 2 11 Graph Transformations Questions

Practise applying translations, reflections and stretches to graphs, deriving transformed functions, mapping key features and describing combined transformations precisely.

Exam points

Apply translations, reflections and horizontal or vertical stretches to a graph, using the correct direction, scale factor and order.
Derive the transformed function from an original formula or recover transformation parameters from a stated graph or key point.
Map intercepts, vertices, periods, domain or range through a transformation and use them to sketch or evaluate the new graph.
Combine several transformations, including compositions where permitted, and describe the complete sequence unambiguously.

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Study SL 2.11—Graph transformations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 3]

Consider the function $f(x)=a x^{3}+b x^{2}+c x+d$ , where $x \in \mathbb{R}$ and $a, b, c, d \in \mathbb{R}$ .

State each of the transformations in the order in which they are applied.

(c) translation through $\binom{2}{0}$ ,

Note: This can be seen anywhere.

EITHER
a stretch scale factor $\frac{1}{2}$ parallel to the y-axis then a translation through $\binom{0}{-4} \quad \boldsymbol{A} 2$
OR
a translation through $\binom{0}{-8}$ then a stretch scale factor $\frac{1}{2}$ parallel to the y-axis A2

Note: Accept 'shift' for translation, but do not accept 'move'. Accept 'scaling' for 'stretch'.

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IB Maths AA HL Sl 2 11 Graph Transformations Questions question 1