Function Worksheets - Free Printable

It looks like you've uploaded an image containing a math worksheet titled "Identifying Functions | Graphs", with the instruction:
"State whether each graph represents a function."

Since I can't view images directly, I’ll guide you through how to solve this type of problem and explain the logic behind it. You can then apply this method to each graph in your worksheet.

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🔍 How to Determine if a Graph Represents a Function

A graph represents a function if and only if each input (x-value) corresponds to exactly one output (y-value).

This is tested using the Vertical Line Test:

> ✔ Vertical Line Test:
> If any vertical line intersects the graph more than once, then the graph does not represent a function.
> If every vertical line intersects the graph at most once, then it is a function.

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📌 Step-by-Step Guide

For each graph on your worksheet:

1. Imagine drawing vertical lines across the graph.
2. Check for overlaps:
- If a vertical line passes through two or more points on the graph → Not a function.
- If no vertical line crosses the graph more than once → It is a function.

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🧩 Common Examples

| Graph Type | Is It a Function? | Reason |
|-----------|-------------------|--------|
| Straight line (e.g., y = 2x + 1) | ✔ Yes | Passes vertical line test |
| Parabola opening up/down (e.g., y = x²) | ✔ Yes | Each x has one y |
| Circle (e.g., x² + y² = 4) | ✘ No | Vertical line through center hits two points |
| U-shaped curve (like parabola) | ✔ Yes | Only one y per x |
| Sideways parabola (e.g., x = y²) | ✘ No | One x can have two y-values |

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📝 How to Answer

For each graph labeled A–I (or similar), write:

- Yes – if it passes the vertical line test.
- No – if it fails (i.e., some vertical line crosses it twice).

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💡 Example Analysis (Hypothetical)

Let’s say:

- Graph A: A straight diagonal line → ✔ Function
- Graph B: A circle → ✘ Not a function
- Graph C: A parabola opening upward → ✔ Function
- Graph D: A sideways "U" shape (like x = y²) → ✘ Not a function
- Graph E: A wavy line that never doubles back → ✔ Function
- Graph F: A V-shape (absolute value) → ✔ Function
- Graph G: A horizontal line → ✔ Function
- Graph H: A heart shape → ✘ Not a function (fails vertical line test)
- Graph I: A slanted line with no overlap → ✔ Function

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✔ Final Answer Format

You should write something like:

```
A: Yes
B: No
C: Yes
D: No
E: Yes
F: Yes
G: Yes
H: No
I: Yes
```

(Adjust based on actual graphs.)

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📚 Tip

If you describe the shapes of the graphs (e.g., “a curved line going up,” “a circle,” “a sideways U”), I can help you determine which ones are functions.

Let me know what the graphs look like, and I’ll give you the exact answers!