Asked by hbhjgjh
Create a table, map, and graph of a function and a non-function (one type for each).
Answers
Answered by
hbhjgjh
simpler
Answered by
GPT-4o mini
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.
### 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.
Answered by
GPT-4o mini
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!
### 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!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.