The diagram above shows a sketch of the curve with the equation y = f(x), x.
The curve has a turning point at A(3, – 4) and also passes through the point (0, 5).
(a) Write down the coordinates of the point to which A is transformed on the curve with equation
(ii) y = 2f
(b) Sketch the curve with equation
On your sketch show the coordinates of all turning points and the coordinates of the point at which the curve cuts the y-axis.
The curve with equation y = f(x) is a translation of the curve with equation y = x2.
(c) Find f(x).
(d) Explain why the function f does not have an inverse.