Section 3.4 – Function transformations MTA120 – Fall 04

On the internet, go to the website www.slu.edu/classes/maymk You should have a number of applets to choose from. Choose the applet for Family of Graphs.

Note – you may have to hit some of the character keys (^,(,),) twice in order for the symbols to appear on the function line. Also, if you do not enter the functions as written below, you will get error messages.

Enter x^2 + c on the function line. (This is the function x² + c). Adjust the scroll bar for c.

1.) What happens to the graph as c becomes negative? – more negative?

2.) What happens to the graph as you adjust c to become positive? – more positive?

Enter (x+b)^2 on the function line. (This is the function (x+b)²). Adjust the scroll bar for b.

1.) What happens to the graph as b becomes negative? – more negative?

2.) What happens to the graph as b becomes positive? - more positive?

Enter a*x^2+b*x+c on the function line (This is the function ax²+bx+c). Adjust the scroll bar for b.

1.) What do you notice as you adjust b? How does the function move?

2.) Return the b scroll bar to 0 and adjust the scroll bar for a. How does the function move?

3.) Return the a scroll bar to 0 and adjust the scroll bar for c. How does the function move?

The above 3 functions use what are called transformations. Adjusting the parameters of a, b, and c in certain functions cause the functions to have certain general movements.

Enter the function a*abs(x).

1.) What happens as you adjust the value of a? (positive?) (negative?)

What generalizations can you draw from the information above. In other words,

1.) What changes to the equation of the function cause the graph to move up and down?

2.) What changes to the function cause the graph to move right to left?

3.) What changes to the equation of the function cause the graph to reflect around the x axis?

How do b and c change -

Enter a*(x+b)^(1/2) + c on the function line. Set b and c to 0. Set the value of a to 1. Always return the value of b and c to 0 between questions.

1.) What function is graphed when you shift this graph up 2 units?

2.) What function is graphed to shift the graph to the right 3 units?

3.) What function is graphed to shift the graph up 2 units and to the right 3 units?

Enter (x + b)^3 + c on the function line.

1.) What function is graphed to shift the graph to the right 4?

2.) What function is graphed to shift the graph up 4?

3.) What function is graphed to shift the graph to the left 4?

4.) What function is graphed to shift the graph down 4?

Return to the Family of Graphs Applet page.
Last modified October 12, 2004, by Mike May, S.J.