Open the Java Graph applet below. Click the sliders ...
Describe how different values of the parameter k influences the graph f1(x) = x³ + kx.

Explain how and why k influences f1(x):
1. by viewing f1(x) as the sum of two functions f2(x) and f3(x).
2. by viewing f1(x) as the product of two functions f2(x) and f3(x).

If needed, you can open the applet below to develop or test your theories ...
Type your own functions in f2(x) and f3(x) and press ENTER.

 

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Open the applet: Compare the meaning of the parameters b and c in the two functions
f1(x) = sin (bx - c) and f2(x) = sin[b(x – c)]. Note: The applet uses radian angle measure!

We start with c = 0, so the graphs are the same, i.e. y = sin bx. Change b - what is the influence of b?

Now reset b to 1 and keep it at 1, so the graphs are the same, i.e. y = sin (x – c). Change c ... What happens?

Now what happens when b and c both change?
Now change b to 2 and keep it constant. Then change c ...
Now change b to 3. Then change c ...
Now change b to 0,5. Then change c ...

Describe the differences in the way f1(x) and f2(x) behave. Which form of the formula is more useful? Why?

Draw the graphs of y = sin (2x – 3) and y = sin 2[(x – 3)] and check it in the applet.