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To determine whether each graph represents a one-to-one function, we can use the **horizontal line test**. A function is one-to-one if each horizontal line crosses the graph at most once. Here’s the analysis:

1. **Graph 1**:
   - This is a parabolic graph that opens upwards.
   - A horizontal line would intersect this curve more than once.
   - **Answer**: No (not one-to-one).

2. **Graph 2**:
   - This graph appears to be a line with a constant negative slope.
   - A horizontal line will only intersect this line at one point.
   - **Answer**: Yes (one-to-one).

3. **Graph 3**:
   - This graph is a wavy curve, likely sinusoidal.
   - A horizontal line would intersect it multiple times.
   - **Answer**: No (not one-to-one).

4. **Graph 4**:
   - This graph consists of individual points (not a continuous function).
   - Some y-values are repeated (e.g., two points have y = 2).
   - **Answer**: No (not one-to-one).

5. **Graph 5**:
   - Similar to Graph 4, it’s a collection of discrete points.
   - There are repeated y-values, so it’s not one-to-one.
   - **Answer**: No (not one-to-one).

6. **Graph 6**:
   - This is a line with a negative slope, representing a linear function.
   - A horizontal line would intersect this line at only one point.
   - **Answer**: Yes (one-to-one).

### Summary:
- **Graph 1**: No
- **Graph 2**: Yes
- **Graph 3**: No
- **Graph 4**: No
- **Graph 5**: No
- **Graph 6**: Yes

Would you like a deeper explanation of one-to-one functions? 

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1. What is the horizontal line test, and how is it used in this context?
2. Can parabolas ever represent one-to-one functions?
3. Why do discrete graphs like Graph 4 and Graph 5 often fail to be one-to-one?
4. What are some characteristics of functions that are always one-to-one?
5. How does the slope of a line relate to its status as a one-to-one function?

**Tip**: Remember, if a function is strictly increasing or decreasing over its domain, it is one-to-one by definition!

For each function graphed, state whether it is one-to-one.

Learn how to determine whether a function is one-to-one using the horizontal line test. This problem covers a variety of graph types, including linear, parabolic, sinusoidal, and discrete graphs. Suitable for high school students (Grades 9-12).

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