Think about the three representations of functions you learned above. Create a table, map, and graph of a function and a non-function (one type for each). After you have created and shared your own representations, identify the relationships shared by two of your peers.

Answer 1

Let's create a table, a mapping diagram, and a graph for a function and a non-function.

Function: f(x) = x²

1. Table Representation

| x | f(x) | |----|------| | -2 | 4 | | -1 | 1 | | 0 | 0 | | 1 | 1 | | 2 | 4 |

2. Mapping Diagram

x:    -2          -1          0          1          2
       |           |          |          |          |
       |           |          |          |          |
f(x):  4          1          0          1          4

3. Graph Representation

  |
4 |         *
  |       *   *
2 |     *       *
  |   *           *
0 | *               *
  |____________________
    -2 -1  0  1  2  

Non-Function: Circle Equation x² + y² = 4

1. Table Representation

| x | y | |----|-----| | -2 | 0 | | 0 | 2 | | 0 | -2 | | 1 | √3 | | 1 | -√3 | | 2 | 0 |

2. Mapping Diagram

x:    -2           0          1          2
       |            |          |          
       |            |          |
y:    0            2          √3
       |            |
       |            |
y:    0            -2         -√3

3. Graph Representation

  |
  |          *        *
  |      *              *
  |    *                  *
  |  *                      *
  | *                        *
0 |*__________________________*_______
  |                            *  *
  |                          *      *
  |                        *          *
  |                      *              *
  |                    *                  *
  |___________________*____________________
        -2 -1  0  1  2  

Relationships Shared by Peers

Once you see the representations created by your peers, you can identify similarities or differences in their functions and non-functions. For example:

• Function Relationship: If a peer selected a linear function, you might note how both your function and theirs provide a unique output for every input (one-to-one).
• Non-Function Relationship: If another peer selected a parabolic function for their non-function, you could discuss how both representations (the circle and their parabola) fail the vertical line test, thus not being functions.

This exercise helps to solidify the understanding of functions versus non-functions through different representations.