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To find the domain and range of the function represented by the graph:

### 1. **Domain**:
   The domain of a function is the set of all possible input values (x-values) for which the function is defined.

   - Observing the graph, the function starts at \(x = -2\) and goes up to \(x = 7\).
   - There are no breaks in the graph within this interval, meaning the function is defined for all \(x\) from \(x = -2\) to \(x = 7\).
   - Therefore, the domain is: 
   \[
   \text{Domain} = [-2, 7]
   \]

### 2. **Range**:
   The range of a function is the set of all possible output values (y-values) that the function can produce.

   - The lowest point on the graph is at \(y = -2\) (when \(x \approx -1.8\)).
   - The highest point on the graph is at \(y = 6\) (when \(x = 7\)).
   - The function takes all values from \(y = -2\) to \(y = 6\).
   - Therefore, the range is:
   \[
   \text{Range} = [-2, 6]
   \]

Would you like more details on this, or do you have any other questions?

### Follow-up Questions:
1. What happens to the domain and range if the function has vertical asymptotes?
2. How would the domain change if there were a hole in the graph at a certain x-value?
3. Can you find the intervals of increase and decrease for this function?
4. How does the range change if we apply a vertical shift to the function?
5. What is the significance of closed and open dots in defining the domain and range?

### Tip:
Always check for any gaps, holes, or asymptotes in the graph to accurately determine the domain and range of a function.

Learn how to find the domain and range of a function using graph analysis. Understand the concepts of domain (input values) and range (output values) with clear examples and step-by-step explanations. Suitable for high school students and anyone interested in understanding function properties.

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