Module 1 Transformations

Benchmark - Combinations

Benchmark assignments give you a chance to practice to the level required for this section. Detailed solutions are provided.

1. Describe how the graph of each of the following functions can be obtained from the graph of y = f(x). ( 4 marks)

a) y = f(-x + 2)
b) y = f(2x + 8 ) - 4
c) y = f(4 - x) + 5
d) y - 8 = f(3x - 6)

2. The height, y meters, of an emergency flare fired upward from a small boat can be modelled by the function:
y = -5(x - 4)² + 80
where x seconds is the time since the flare was fired. (4 marks)
a) Describe how the graph of y = -5(x - 4)² + 80 can be obtained by the transformation of y = x².
b) Interpret the equation of the transformed function to find the maximum height reached by the flare and the time it takes to reach this height.

3. Describe how the graph of y = 4cos(2(x - 3)) + 1 is related to the graph of y = cos x. (2 marks)