Answer:
f(x) → f(x - b) means shift the function b units to right
Therefore x² → (x - 2)² means the function is moved 2 units to the right.
f(x) → a f(x) means a vertical stretch
Therefore (x - 2)² → 2(x - 2)² means the function stretched vertically by a scale factor of 2.
f(x) → f(x) + b means shift the function b units up
Therefore 2(x - 2)² + 1 means the function is moved 1 unit up.
Attached diagram:
f(x) is shown in black, g(x) is shown in red.
Points to help plot graph f(x):
(-3, 9) (-2, 4) (0, 0) (2, 4) (3, 9)
Points to help plot graph g(x):
(0, 9) (2, 1) (4, 9)
