Below is an exploration and discussion of the above function for different values of a, b, and c.
Below is the graph for a=1, b=1, and c=1.
What happens if we leave a=b=c but try values larger than 1? Below is a graph for a=b=c=2. Notice that the period, wave length, and amplitude have all changed.
Let's change one variable at a time so we can determine what varying a, b, and c does to the graphs. In the graphs below, b and c are kept constant at 1 and a changes. For a graping calculator movie that shows the curve for values of a from -10 to 10 click here. In the graph below, Green: a=-1, Purple: a=1, Red: a=2, Blue: a=3. Notice that changing a causes the amplitude to change.
Now, let's look at what happens when we keep a and c constant at 1 and vary b. For a graphing calculator move that shows the curve for values of b from -10 to 10 click here. In the graph below, Purple: b=-1, Red: b=1, Blue: b=2, and Green: b=3. Notice that varying b causes the wave length to change.
In the graph below, a and b are kept constant at 1 and c changes. For a graphing calculator move that shows the curve for values of c from -10 to 10 click here. In the graph below, Purple: c=-1, Red: c=1, Blue: c=2, and Green: c=3. Notice that changing c causes a change in the period.
