Question

Create a table, map, and graph of a function and a non-function (one type for each).

Answer 1

Certainly! Below are examples of a function and a non-function, including their respective tables, graphs, and a basic description.

### Function

**Definition**: A function is a relation where each input (x) has exactly one output (y).

**Example Function**: \( f(x) = 2x + 3 \)

#### Table
| x | f(x) |
|---|------|
| -2| -1 |
| -1| 1 |
| 0| 3 |
| 1| 5 |
| 2| 7 |

#### Graph

### Non-Function

**Definition**: A non-function fails the vertical line test, meaning there is at least one input (x) that has more than one output (y).

**Example Non-Function**: The relation defined by the equation \( y^2 = x \)

#### Table
| x | y |
|---|---------|
| 0 | 0 |
| 1 | 1 |
| 1 | -1 |
| 4 | 2 |
| 4 | -2 |

#### Graph

### Summary
- **Function**: A relationship where each input corresponds to exactly one output (example: linear function \( f(x) = 2x + 3 \)).
- **Non-Function**: A relationship where a single input can correspond to multiple outputs (example: the equation \( y^2 = x \)).

### Note
The graphs provided are conceptual illustrations. For accurate graphing, you may want to use a software tool such as Desmos or GeoGebra. The image links are placeholders for the purpose of this example.

Answer 2

simpler

Answer 3

Sure! Let’s simplify the explanation and examples.

### Function Example

**Function**: A relation where each input has exactly one output.

#### Function: \( f(x) = x + 1 \)

#### Table
| x | f(x) |
|---|------|
| 0 | 1 |
| 1 | 2 |
| 2 | 3 |
| 3 | 4 |
| 4 | 5 |

#### Graph
A graph of the function \( f(x) = x + 1 \) looks like this:

```
y
^
|
| *
| *
| *
| *
| *
+--------------> x
0 1 2 3 4
```

### Non-Function Example

**Non-Function**: A relation where an input can have multiple outputs.

#### Example: Vertical Line Test (e.g., a circle)

- **Equation**: \( x^2 + y^2 = 1 \)

#### Table
| x | y |
|-----|-------|
| 0 | 1 |
| 0 | -1 |
| 1 | 0 |
| -1 | 0 |
| √0.5| √0.5 |
| √0.5| -√0.5 |

#### Graph
A graph of the non-function (circle) looks like this:

```
y
^
| *
| * *
| * *
| * *
| * *
| *
+--------------> x
```

### Summary
- **Function**: Each input (x) has one output (e.g., \(f(x) = x + 1\)).
- **Non-Function**: An input can have multiple outputs (e.g., a circle \( x^2 + y^2 = 1 \)).

Let me know if you need any further simplifications!