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.