CAIE A-Level Mathematics 1.2.5 Graph Transformations

CAIE A-Level Mathematics 1.2.5 Graph Transformations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise translating, reflecting and stretching y = f(x), converting between equations and verbal descriptions and applying combined transformations in the correct order.

How this is tested

  • distinguish changes outside f from horizontal changes inside its argument
  • state stretch direction and scale factor or give a translation vector with both components
  • apply combined transformations in order and write the resulting equation such as 3f(−x)

Question 3

Question 3(a)

(a)

The graph of y=f(x) is transformed to the graph of y=f(3 x)+2.
Describe fully the two transformations which have been combined to give the resulting graph.

[ 3 ]

Question 3(b)

(b)

A different graph has equation y=g(x). This graph is stretched by scale factor 3 in the y-direction and then reflected in the y-axis.

Write down the equation of the transformed graph in terms of the function g.

[ 2 ]