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!