The image contains several examples related to
relations and functions, which are fundamental concepts in algebra. Let's analyze each part of the image step by step:
---
1. Table Representation
The first table shows the following data:
| \( x \) | \( y \) |
|---------|---------|
| 5 | 1 |
| 5 | 2 |
| 5 | 3 |
| 5 | 4 |
####
Analysis:
- Here, the input \( x \) is always 5, but the output \( y \) varies (1, 2, 3, 4).
- This relationship is a
relation because one input (\( x = 5 \)) corresponds to multiple outputs (\( y = 1, 2, 3, 4 \)).
- However, it is
not a function because a function must have exactly one output for each input. In this case, \( x = 5 \) maps to multiple \( y \)-values.
---
2. Mapping Diagram
The mapping diagram shows the following pairs:
- Input: 6 → Output: 9
- Input: 8 → Output: 11
- Input: 11 → Output: 15
- Input: 14 → Output: 20
####
Analysis:
- Each input value (6, 8, 11, 14) maps to exactly one output value (9, 11, 15, 20).
- This satisfies the definition of a
function: every input has exactly one corresponding output.
- Therefore, this is a
function.
---
3. Second Table Representation
The second table shows the following data:
| \( x \) | \( y \) |
|---------|---------|
| 6 | -4 |
| 8 | 2 |
| 10 | 6 |
| 12 | -4 |
| 14 | 11 |
####
Analysis:
- Each input value (\( x = 6, 8, 10, 12, 14 \)) maps to exactly one output value (\( y = -4, 2, 6, -4, 11 \)).
- Even though the output value \(-4\) appears twice (for \( x = 6 \) and \( x = 12 \)), this does not violate the definition of a function because each input still has exactly one output.
- Therefore, this is a
function.
---
4. Graph Representation
The graph shows a set of points:
- (6, 9)
- (8, 11)
- (11, 15)
- (14, 20)
####
Analysis:
- The points on the graph correspond to the same pairs as the mapping diagram in part 2.
- Since each \( x \)-value (input) is paired with exactly one \( y \)-value (output), this represents a
function.
- Visually, you can confirm this using the
vertical line test: any vertical line drawn on the graph will intersect the points at most once, indicating that it is a function.
---
Summary of Results
1. The first table represents a
relation but
not a function because one input (\( x = 5 \)) corresponds to multiple outputs.
2. The mapping diagram represents a
function because each input has exactly one output.
3. The second table represents a
function because each input has exactly one output.
4. The graph represents a
function because it passes the vertical line test.
---
Final Answer
\[
\boxed{\text{The first table is not a function, while the others are functions.}}
\]
Parent Tip: Review the logic above to help your child master the concept of relations and functions worksheet pdf.
![Determine If A Relation Is A Function Worksheets [PDF] (8.F.A.1 ...](/images2/relations-and-functions-worksheet-pdf/relations-and-functions-worksheet-pdf-16.png)
