https://file.aiquickdraw.com/mathbot/file/17267751713880xg9qje9.jpg

Looking at the provided graph, I see a parabola that opens upwards. Let's determine the **domain** and **range** based on the shape and position of the graph.

1. **Domain**: The domain of a function refers to all possible \(x\)-values (inputs) for which the function is defined.
   - From the graph, the parabola seems to extend infinitely left and right, which means the function is defined for all real numbers.
   - Therefore, the **domain** is all real numbers, which in interval notation is written as: 
     \[
     (-\infty, \infty)
     \]
   So the correct choice for the domain is **A**, and the domain of the function is \( (-\infty, \infty) \).

2. **Range**: The range of a function refers to all possible \(y\)-values (outputs).
   - The parabola has a minimum point at \( y = -8 \), and from there it extends upwards. Therefore, the \(y\)-values (range) start at \(-8\) and go up to positive infinity.
   - The range in interval notation is:
     \[
     [-8, \infty)
     \]
   So the correct choice for the range is **B**, and the range of the function is \( [-8, \infty) \).

### Would you like more details, or do you have any questions?

Here are 5 related questions to explore:
1. How do you determine the vertex of a parabola from its graph?
2. What is the difference between domain and range?
3. Can a function have a limited domain but an infinite range?
4. How can you write the domain and range for a function given its equation rather than its graph?
5. What are some real-life applications of determining a function's domain and range?

**Tip**: Always check the behavior of the graph at extreme points to correctly identify the domain and range!

Use the graph to determine the domain and range of the function.

This problem involves determining the domain and range of a function based on a graph of a parabola. The graph shows a function with a domain covering all real numbers and a range starting from the minimum value at y = -8 and extending upwards. Suitable for students in Grades 9-11 learning about functions and graphing.

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