Visualizing Functions: More examples to Study and Compare
Here are more examples of tables, equations, transformation figures and cartesian graphs . On the left are the tables of values for the functions evaluated at selected points. The functions are also described by equations where the variable y is a function of the variable x, y = f (x). In the center are the corresponding cartesian graphs and on the right you will see the related sampling of data visualized with a transformation figure. *

As you read through these examples, write a description for each example of the features you find particularly distinctive in that example.

Example 2.  f (x) = x
 x f(x)=x 2 2 1 1 0 0 -1 -1 -2 -2  Example 3.   f (x) = - x
 x f(x)=-x 2 -2 1 -1 0 0 -1 1 -2 2  Example 4.  f (x) = |x|
 x f(x)=|x| 2 2 1 1 0 0 -1 1 -2 2  Example 5.  f (x) = 2x
 x f(x)=2x 2 4 1 2 0 0 -1 -2 -2 -4  Example 6.  f (x) = x+1
 x f(x)=x+1 2 3 1 2 0 1 -1 0 -2 -1  Example 7.  f (x) = x 2
 x f(x)=x 2 2 4 1 1 0 0 -1 1 -2 4  Example 8.  f (x) = 1/x
 x f(x)=1/x 2 0.5 1 1 0 ?? -1 -1 -2 -0.5  Example 9.    f (x) = 2x
 x f(x)=2x 2 4 1 2 0 1 -1 0.5 -2 0.25  Example 10. f (x) = 3
 x f(x)=3 2 3 1 3 0 3 -1 3 -2 3  Example 11. f (x) =-2x + 1
 x f(x)=-2x+1 2 -3 1 -1 0 1 -1 3 -2 5  * The graphs and figures in this section were made using the freeware Winplot . You can find out more about Winplot by clicking on the name.