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.

Question

In your response to each post:

Identify the type of representation.
Identify if it is a function or non-function.

Answer 1

Sure! Below are the representations for a function and a non-function:

Function Representation

1. Table: | Input (x) | Output (y) | |-----------|------------| | 1 | 2 | | 2 | 4 | | 3 | 6 | | 4 | 8 |

2. Mapping:

   • {1 → 2, 2 → 4, 3 → 6, 4 → 8}

3. Graph:

   • The graph of the function y = 2x
   • Points: (1, 2), (2, 4), (3, 6), (4, 8)
   • The graph is a straight line with a slope of 2.

Non-Function Representation

1. Table: | Input (x) | Output (y) | |-----------|------------| | 1 | 2 | | 1 | 3 | | 2 | 4 | | 3 | 6 |

2. Mapping:

   • {1 → {2, 3}, 2 → 4, 3 → 6}

3. Graph:

   • The graph of the relation {(1, 2), (1, 3), (2, 4), (3, 6)}
   • The points (1, 2) and (1, 3) indicate that the input 1 corresponds to two different outputs, which fails the vertical line test.

Summary:

• The first set of representations (table, mapping, graph) corresponds to a function because each input is paired with exactly one output.
• The second set of representations corresponds to a non-function as the input 1 leads to two different outputs (2 and 3).

If you have posts by peers, you can follow this style to respond to them, identifying their representation type and whether they represent a function or non-function.