ANSWERS:
1) Horizontally compressed by a factor of ¹/₂ - TRUE
2) Phase shift left π/2 units - FALSE
3) Vertically compressed by a factor of -3 - FALSE
4) Vertically shifted up 4 units - TRUE
5) The period of the function h is half the period of the parent function - TRUE
6) Amplitude 3 times greater than the parent function - TRUE
SOLUTION:
The function is given to be:
[tex]h(x)=-3\cos (2x-\pi)+4[/tex]
The parent function is:
[tex]f(x)=\cos (x)[/tex]
Comparing with the parent function, the following transformations took place:
1) The function is horizontally compressed by a factor of ¹/₂.
2) The function undergoes a phase shift of π units to the right.
3) The function is vertically stretched by a factor of -3 units.
4) The function is shifted upwards by 4 units.
The graph of the function is shown below:
The green graph is the parent function while the blue graph is the transformed one.
The period of the transformed function is half that of the parent function. The amplitude of the transformed function is 3 times greater than the parent function.
ANSWERS:
1) Horizontally compressed by a factor of ¹/₂ - TRUE
2) Phase shift left π/2 units - FALSE
3) Vertically compressed by a factor of -3 - FALSE
4) Vertically shifted up 4 units - TRUE
5) The period of the function h is half the period of the parent function - TRUE
6) Amplitude 3 times greater than the parent function - TRUE
