
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Transcribed Image Text:# Input/Output Tables and Functions
## Explanation
In this exercise, five input/output tables are provided. The objective is to identify which of these tables represent functions. A function is defined as a relation where each input has a unique output.
### Input/Output Tables
**Table 1**
| Input | Output |
|-------|--------|
| 1 | 4 |
| 2 | 4 |
| 3 | 4 |
| 4 | 4 |
**Table 2**
| Input | Output |
|-------|--------|
| -1 | 0 |
| -1 | 1 |
| -1 | 2 |
| -1 | 3 |
**Table 3**
| Input | Output |
|-------|--------|
| 1 | 2 |
| 2 | 1 |
| 3 | 2 |
| 4 | 1 |
**Table 4**
| Input | Output |
|-------|--------|
| 0 | 0 |
| -1 | 1 |
| 1 | 1 |
| -2 | 4 |
| 2 | 4 |
**Table 5**
| Input | Output |
|-------|--------|
| 0 | 0 |
| 1 | 2 |
| -1 | -2 |
| 2 | 3 |
| 2 | -3 |
### Analysis
- **Table 1**: This table represents a function because each unique input (1, 2, 3, 4) maps to a unique output (4).
- **Table 2**: This table does **not** represent a function because the input -1 maps to multiple outputs (0, 1, 2, 3).
- **Table 3**: This table represents a function because each unique input (1, 2, 3, 4) maps to a unique output (2, 1, 2, 1).
- **Table 4**: This table represents a function because each unique input (0, -1, 1, -2, 2) maps to a unique output (0, 1, 1, 4, 4).
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