To determine the range of a graph, we need to understand the set of all possible output values (y-values) that the graph can take based on its equation or visual representation.

1. **For a graph of a function:** 
   - The range refers to all the y-values that the function attains as x-values vary over its domain.
   
   Example:
   - For \( f(x) = x^2 \), the range is all non-negative real numbers: \( [0, \infty) \), since the lowest point is 0 and the graph extends infinitely upward.

2. **For a given visual graph:**
   - The range can be identified by observing the lowest and highest points on the graph (y-axis).
   - If the graph is bounded (it has a lowest and highest point), the range will be within a certain interval.
   - If the graph extends infinitely in one or both directions, the range will either be infinite or extend to some specific value.

If you have a specific equation or graph in mind, feel free to upload an image or describe it, and I can help find its exact range.

Would you like more details or examples? Here are 5 questions related to this topic:

1. How do you find the range of a quadratic function?
2. What is the range of the function \( f(x) = \sin(x) \)?
3. How does the range of a function differ from its domain?
4. Can a function's range ever be infinite? If so, under what conditions?
5. How can transformations affect the range of a graph?

**Tip:** To determine the range from a graph, always check for asymptotes or restrictions in the y-values!

Discover how to determine the range of a graph by analyzing the possible y-values that a function can take. Explore examples, such as quadratic functions and trigonometric functions, and learn how transformations affect the range. Suitable for high school students in Grades 9-12.

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