https://file.aiquickdraw.com/mathbot/file/1726704653636m7w9dzrm.jpg

To find the domain and range of the function shown in the image, we can analyze the graph:

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

- From the graph, the parabola extends indefinitely to the left and right, meaning there are no restrictions on the x-values. Thus, the domain is:
  \[
  \text{Domain} = (-\infty, \infty)
  \]

### 2. **Range:**
The range refers to the set of all possible output values (y-values) that the function can take.

- The lowest point of the parabola, the **vertex**, appears to be at \( y = 0 \), and the parabola opens upwards. Therefore, the function takes values from \( y = 0 \) and increases indefinitely. Thus, the range is:
  \[
  \text{Range} = [0, \infty)
  \]

Would you like more details on how to derive the domain and range from a graph, or do you have any other questions? Here are some related questions to deepen your understanding:

1. How do we determine if a function's graph extends to infinity?
2. What is the significance of the vertex in a quadratic function?
3. How can we algebraically determine the domain and range of a function without graphing?
4. How does the direction a parabola opens affect its range?
5. What types of functions have limited domains?

**Tip:** When analyzing a quadratic function from its graph, the vertex is a key feature in determining the range, especially for parabolas.

Find domain and range for the function shown in the image.

Learn how to find the domain and range of a quadratic function from its graph. This problem covers algebraic concepts and graph analysis to determine the x and y values, including formulas and theorems. Suitable for students in Grades 8-10.

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