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) = 2^{x}
x

f(x)=2^{x}

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.