The function g is defined by g: x ↦ (x − 2)² − 9, x ∈ ℝ.

a. Draw a sketch of the graph of y = g(x), labelling the turning points and the x- and y-intercepts.

b. Write down the coordinates of the turning point when the curve is transformed as follows:

i. 2g(x − 4)

ii. g(2x)

iii. |g(x)|

c. Sketch the curve with equation y = g(|x|). On your sketch show the coordinates of all turning points and all x- and y-intercepts.