Question

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.
In your response to each post:

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

Answer 1

Here's a breakdown of a function and a non-function with their respective table, map, and graph representations:

### Function Representation

#### Table for Function
| Input (x) | Output (f(x)) |
|-----------|---------------|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

#### Map for Function
```
1 → 2
2 → 4
3 → 6
4 → 8
```

#### Graph for Function (f(x) = 2x)
*This is a linear function where each input has a unique output.*

### Non-Function Representation

#### Table for Non-Function
| Input (x) | Output (y) |
|-----------|----------------|
| 1 | 2 |
| 1 | 3 |
| 2 | 4 |
| 3 | 6 |

#### Map for Non-Function
```
1 → 2, 3
2 → 4
3 → 6
```

#### Graph for Non-Function (a vertical line test)
*This is a relation where the input '1' corresponds to two different outputs (2 and 3), making it a non-function.*

### Summary

- **Function Representation**:
- Type: Table, Map, Graph
- This is a function (f(x) = 2x) because each input has a unique output.

- **Non-Function Representation**:
- Type: Table, Map, Graph
- This is a non-function because the input '1' maps to two outputs (2 and 3), violating the definition of a function that states each input must correspond to exactly one output.

Answer 2

can you make it into a paragraph

Answer 3

Sure!

In the study of functions and non-functions, we can represent each using various methods such as tables, maps, and graphs. For a function, consider the linear relationship defined by the equation \( f(x) = 2x \). In a table representation, the input-output pairs are as follows: when the input is 1, the output is 2; when the input is 2, the output is 4; for an input of 3, the output is 6; and for an input of 4, the output becomes 8. The mapping representation shows that 1 corresponds to 2, 2 corresponds to 4, 3 corresponds to 6, and 4 corresponds to 8, illustrating that each input has a unique output. This relationship can also be visually represented on a graph, which displays a straight line indicating a consistent output for each input. Conversely, for a non-function, we have a set of input-output pairs in a table where the input of 1 leads to two different outputs: 2 and 3, while the input of 2 results in an output of 4 and an input of 3 gives an output of 6. The mapping for this non-function indicates that the input 1 points to both 2 and 3, which violates the function's requirement of having only one output for each input. This relationship fails the vertical line test when graphed, as a vertical line intersects the curve at more than one point at x = 1, proving it to be a non-function. Thus, we clearly see the distinction between a function and a non-function through these different representations.

Answer 4

can you write it like a kid

Answer 5

Sure! Here’s a simpler way to explain it:

Let’s talk about a function and a non-function using some fun examples! For a function, think about a special machine that takes a number, does something to it, and gives you a different number back. For instance, if our machine takes a number \( x \) and multiplies it by 2 (like \( f(x) = 2x \)), we can make a little table. If we put in 1, we get 2; if we put in 2, we get 4; if we put in 3, we get 6; and if we put in 4, we get 8! So, each number we put in gives us just one answer, which makes it a function!

Now, let's talk about a non-function, which is a bit tricky. Imagine we have another table where if we put in the number 1, the machine can give us either 2 or 3. This means the same number (1) can lead to two different answers. We can also write it like a map where 1 points to both 2 and 3, which is confusing! When we graph this, if we draw a vertical line at the number 1, it touches the graph at two spots, which means it’s not a function. So, a function is like a magic machine that only gives one answer for each number, while a non-function can be a tricky one that gives different answers for the same number!