Relations and Functions worksheet with multiple representations and graph analysis.

It looks like you've uploaded a worksheet titled "Practice Worksheet: Relations & Functions" that includes several tasks related to identifying whether given relations are functions, determining domains and ranges, and analyzing graphs. However, I can't directly view or access images or files you upload.

But since you've described the content, I’ll help you solve the problems based on typical formats of such worksheets. Let's go through each section step by step and explain how to solve them.

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Section 1: Complete the Table, Graph, Mapping Diagram, and Determine if it’s a Function

This section likely has a set of ordered pairs (x, y) for each problem. For example:

#### Example Problem:
Given:
- Relation: {(2, 3), (4, 5), (6, 7)}

You would complete:

1. Table:
| x | y |
|---|---|
| 2 | 3 |
| 4 | 5 |
| 6 | 7 |

2. Graph: Plot the points (2,3), (4,5), (6,7) on a coordinate plane.

3. Mapping Diagram: Draw two ovals — one for x-values, one for y-values. Draw arrows from each x to its corresponding y.

4. Function? → Yes, because each x-value maps to exactly one y-value.

> ✔ A relation is a function if each input (x) has only one output (y).

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Section 2: Determine if Each Graph Shows a Function or Relation

You’re given three graphs. Use the Vertical Line Test to determine if they are functions.

#### Graph 1: A line with a positive slope (like y = x + 1)
- Domain: All real numbers (or based on graphed portion; e.g., [-3, 3] if bounded)
- Range: All real numbers
- Function? ✔ Yes, because any vertical line crosses the graph at most once.

#### Graph 2: A circle (e.g., x² + y² = 9)
- Domain: [-3, 3]
- Range: [-3, 3]
- Function? ✘ No, because a vertical line (e.g., x = 0) intersects the circle at two points (top and bottom). This fails the Vertical Line Test.

> ⚠️ Circles are relations, not functions.

#### Graph 3: A curved line (e.g., a parabola opening up or sideways?)
Let’s assume it's a parabola opening upward (like y = x²):

- Domain: All real numbers
- Range: [0, ∞) (if vertex at origin)
- Function? ✔ Yes, passes the vertical line test.

If it were a sideways parabola (e.g., x = y²), then it would not be a function.

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Summary of Answers (Typical Format):

#### Graph 1 (Line):
- Domain: $(-\infty, \infty)$ or interval based on graph
- Range: $(-\infty, \infty)$ or appropriate interval
- Function? Yes

#### Graph 2 (Circle):
- Domain: $[-3, 3]$
- Range: $[-3, 3]$
- Function? No

#### Graph 3 (Parabola):
- Domain: $(-\infty, \infty)$
- Range: $[0, \infty)$
- Function? Yes

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🔍 How to Solve These Problems:

1. Use the Vertical Line Test:
- If any vertical line crosses the graph more than once → Not a function.
- If every vertical line crosses at most once → Function.

2. Domain: All possible x-values shown on the graph.
3. Range: All possible y-values shown on the graph.

4. For tables or mapping diagrams:
- Check if any x-value appears more than once with different y-values → Not a function.
- If all x-values are unique → It is a function.

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If you can provide specific details about the problems (e.g., the actual coordinates or descriptions of the graphs), I can give exact answers tailored to your worksheet.

Let me know if you'd like help with a particular part!