1. The diagram above shows a sketch of the curve with the equation y = f(X), X. The curve has a turning point at A

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

(i)

(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.