Vertical Stretching and Compression(scaling) of Graphs

The function to be analyzed is of the form a*f(x). In this tutorial you may use f(x) = ||x|-2| (a "W" shaped graph), f(x) = x² or f(x) = x³.



TUTORIAL

How does the multiplication of a function by a positive constant affect the graph of this function ?

1-Use the scrollbar to set the constant a to different values and observe the effect on the graph.

What is the range of values of the constant that create a vertical compression?

What is the range of values of the constant that create a vertical stretching?

What values reflect the graph on the x axis?

Explain analytically.

You have the choice (left panel, top) of any of the three functions
f(x) = ||x|-2| (this has a "W" shaped graph), f(x) = x² or f(x) = x³.

• Explore the horizontal shift of the graph of a function. Horizontal Shift of Graphs
  
  
• Explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a. Horizontal Stretching and Compression
  
  
• Explore interactively the vertical shifting of the graph of a function. Vertical Shifting/translation of Graphs