Functions and graph transformations – Year 11 GCSE maths test to download as PDF

\(f(x)=2x^2-3\).

1. Work out \(f(4)\). (1 mark)
2. Solve \(f(x)=15\). (3 marks)

\(f(x)=x+4\) and \(g(x)=3x\).

1. Find \(fg(x)\) and \(gf(x)\). (2 marks)
2. Solve \(fg(x)=gf(x)\) and comment on your answer. (2 marks)

\(f(x)=\dfrac{x-5}2\).

1. Find \(f^{-1}(x)\). (2 marks)
2. Work out \(f^{-1}(7)\) and check that \(f(f^{-1}(7))=7\). (2 marks)

The graph of \(y=f(x)\) has a maximum point at \((3,6)\).

1. Write the maximum point on \(y=f(x-2)\) and \(y=f(x)+4\). (2 marks)
2. Write the coordinates of the turning point on \(y=-f(x)\) and say if it is a maximum or minimum. (2 marks)

\(g(x)=x^2-6x+5\).

1. Write \(g(x)\) in the form \((x+a)^2+b\). (2 marks)
2. State the transformation that maps \(y=x^2\) to \(y=g(x)\) and the minimum value of \(g\). (2 marks)