https://file.aiquickdraw.com/mathbot/file/1725374710155dzi92g9y.jpg

The image shows a parabolic graph that appears to be a quadratic function. Let's break down the questions:

1. **D: Domain**
   - The domain (D) represents all the possible x-values for the function. Since this is a quadratic function (a parabola), the domain will include all real numbers.
   - **D = (-∞, ∞)**

2. **R: Range**
   - The range (R) represents all possible y-values for the function. The parabola opens upwards, and its minimum point (vertex) is at \( y = -2 \). Therefore, the range starts from this minimum value and goes upwards to positive infinity.
   - **R = [-2, ∞)**

3. **\( f(3) \)**
   - To find \( f(3) \), we need to locate where \( x = 3 \) on the graph. From the image, when \( x = 3 \), the corresponding \( y \)-value is 2. Therefore, \( f(3) = 2 \).

### Final Answers:
- **D: (-∞, ∞)**
- **R: [-2, ∞)**
- **\( f(3) = 2 \)**

Would you like any further clarification or details?

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Here are five follow-up questions to expand your understanding:

1. What is the vertex form of a quadratic function?
2. How do you determine the axis of symmetry of a parabola?
3. What is the effect of changing the coefficient of \( x^2 \) in a quadratic function?
4. How can you find the roots of the quadratic function shown?
5. How does the range of a quadratic function change if the parabola opens downwards?

**Tip:** The domain of a quadratic function is always all real numbers, but the range depends on whether the parabola opens upwards or downwards.

Find the domain, range, and f(3) of the given quadratic function based on its graph.

Learn how to determine the domain, range, and specific function values from the graph of a quadratic function. This tutorial covers essential concepts for students in Grades 9-10, focusing on interpreting parabolas.

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