Which is a table of ordered pairs defined by y = -4x + 2

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question: Which is a table of ordered pairs defined by y = -4x + 2 

### Function Tables in Mathematics

Below are several tables depicting different functions through sets of input values \( x \) and their corresponding output values \( f(x) \). Each table represents a unique function.

#### Table 1
| \( x \) | \( f(x) \) |
|:-------:|:----------:|
| 0       | 2          |
| 2       | -6         |
| 4       | -14        |
| 6       | -22        |

**Description:** 
This table represents a function where the output decreases with increasing input values. As \( x \) increases, \( f(x) \) becomes more negative.

#### Table 2
| \( x \) | \( f(x) \) |
|:-------:|:----------:|
| 3       | 8          |
| 2       | 12         |
| 4       | -14        |
| 7       | -22        |

**Description:** 
This table depicts a function with non-monotonic behavior, meaning the output values do not uniformly increase or decrease with the input values.

#### Table 3
| \( x \) | \( f(x) \) |
|:-------:|:----------:|
| 0       | 4          |
| 2       | 8          |
| 4       | -14        |
| 6       | 16         |

**Description:** 
This function shows an interesting pattern where the outputs start off positive, become negative, and then become positive again. It indicates a more complex relationship between \( x \) and \( f(x) \).

#### Table 4
| \( x \) | \( f(x) \) |
|:-------:|:----------:|
| 0       | 2          |
| 2       | 16         |
| 4       | -14        |
| 6       | -22        |

**Description:** 
In this table, the function produces a positive output at \( x = 0 \) and \( x = 2 \), but the output decreases sharply to negative values afterward.

### Analyzing Function Tables

Each of these tables represents a different function with its unique characteristics. When analyzing such tables, it's essential to observe the patterns in the output values and how they change as the input values change. This can help in understanding the behavior of the function and might provide
Transcribed Image Text:### Function Tables in Mathematics Below are several tables depicting different functions through sets of input values \( x \) and their corresponding output values \( f(x) \). Each table represents a unique function. #### Table 1 | \( x \) | \( f(x) \) | |:-------:|:----------:| | 0 | 2 | | 2 | -6 | | 4 | -14 | | 6 | -22 | **Description:** This table represents a function where the output decreases with increasing input values. As \( x \) increases, \( f(x) \) becomes more negative. #### Table 2 | \( x \) | \( f(x) \) | |:-------:|:----------:| | 3 | 8 | | 2 | 12 | | 4 | -14 | | 7 | -22 | **Description:** This table depicts a function with non-monotonic behavior, meaning the output values do not uniformly increase or decrease with the input values. #### Table 3 | \( x \) | \( f(x) \) | |:-------:|:----------:| | 0 | 4 | | 2 | 8 | | 4 | -14 | | 6 | 16 | **Description:** This function shows an interesting pattern where the outputs start off positive, become negative, and then become positive again. It indicates a more complex relationship between \( x \) and \( f(x) \). #### Table 4 | \( x \) | \( f(x) \) | |:-------:|:----------:| | 0 | 2 | | 2 | 16 | | 4 | -14 | | 6 | -22 | **Description:** In this table, the function produces a positive output at \( x = 0 \) and \( x = 2 \), but the output decreases sharply to negative values afterward. ### Analyzing Function Tables Each of these tables represents a different function with its unique characteristics. When analyzing such tables, it's essential to observe the patterns in the output values and how they change as the input values change. This can help in understanding the behavior of the function and might provide
The table below represents a function \( f(x) \) with a set of given inputs \( x \) and their corresponding outputs \( f(x) \).

| \( x \) | \( f(x) \)  |
|-----|--------|
| 5   | 12     |
| 2   | 16     |
| 4   | -14    |
| 6   | -22    |

This table indicates how the function \( f(x) \) maps specific input values to their respective output values. Here’s the interpretation:

- When \( x \) is 5, \( f(x) \) is 12.
- When \( x \) is 2, \( f(x) \) is 16.
- When \( x \) is 4, \( f(x) \) is -14.
- When \( x \) is 6, \( f(x) \) is -22.

To understand the behavior of the function, one could plot these points on a graph to see the pattern or trend, analyze the mathematical relationship between the input and output values, or use them for further mathematical calculations or modeling.
Transcribed Image Text:The table below represents a function \( f(x) \) with a set of given inputs \( x \) and their corresponding outputs \( f(x) \). | \( x \) | \( f(x) \) | |-----|--------| | 5 | 12 | | 2 | 16 | | 4 | -14 | | 6 | -22 | This table indicates how the function \( f(x) \) maps specific input values to their respective output values. Here’s the interpretation: - When \( x \) is 5, \( f(x) \) is 12. - When \( x \) is 2, \( f(x) \) is 16. - When \( x \) is 4, \( f(x) \) is -14. - When \( x \) is 6, \( f(x) \) is -22. To understand the behavior of the function, one could plot these points on a graph to see the pattern or trend, analyze the mathematical relationship between the input and output values, or use them for further mathematical calculations or modeling.
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