,its amplitude, period and phase shift are explored interactively using an applet. The investigation is carried out by changing the parameters a, b, c and d. To deeply understand the effects of each parameter on the graph of the function, we change one parameter at the time at the start. Then later we may change more than one parameter.
Exploration and understanding of the phase shift is done by comparing the shift between the graphs of the two functions:
How do the 4 coefficients a,b,c and d affect the graph of f(x)?
use the scrollbar to set a=1,b=1,c=0 and d=0. Write down f(x) and take note of the amplitude, period and phase shift of f(x)? Now change a , how does it affect the graph? The amplitude is defined as |a|.
set a=1,c=0,d=0 and change b. Find the period from the graph and compare it to 2pi/|b|. How does b affect the graph of f(x)? The period is the horizontal distance (along the x-axis) between two points: one is the starting point of a cycle and the second is the end point of the same cycle.