TRANSFORMATIONS OF FUNCTIONS

This applet draws graphs of functions that contain constants a and b for different values of those constants. It illustrates how changing constants causes vertical and horizontal shifts, and vertical stretches.

Example 1

In this example we look at the family of functions y=f(x), where f(x)=(x-a)^2+b; that is:

How is the graph of y=f(x) affected when constants a and b change? You can examine it for yourself. The values of these constants can be changed using the sliders at the bottom of the applet. Observe how changing a and b affects the graph of the function. Notice the direction of the shifts for positive and negative values of a and b.

Do not type in the white field where the function (x-a)^2+b is displayed! Use the sliders at the bottom of the box to change the values of the constants a and b!

Example 2

The second example deals with the family of functions y=b/((x-a)^2 +1); that is:

The initial setting is with b=0. Then, y=0 and the graph of the function (in magenta) is a horizontal line coinciding with the x-axis. As long as b=0, changing the constant a will not make any difference. Why? Start changing b. Observe the effects of larger and larger positive b and changing a. How about negative values for b? What happens to the graph then?

Do not type in the white field where the function b/((x-a)^2+1) is displayed! Use the sliders at the bottom of the box to change values of the constants a and b!