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Write the domain as an inequality and write the range as an inequality

To analyze the graph, I will extract the domain and range information visually from the uploaded image and write the inequalities.

### Step 1: Analyze the Graph
- The graph represents a function that appears to be quadratic, starting from the point \((-3, -3)\) and increasing as it moves to the right.
- The curve is graphed only for \(x \geq -3\), and it is open to the right. This indicates that the function has a starting point at \(x = -3\) but no endpoint in the positive direction, suggesting the domain is restricted to \(x \geq -3\).
- The graph has a minimum value of \(y = -3\) and increases without bound, so the range is \(y \geq -3\).

### Step 2: Write the Domain and Range as Inequalities

- **Domain**: Since the function is defined for \(x\) values starting from \(-3\) and continuing to positive infinity, the domain can be written as:
  \[
  x \geq -3
  \]
  
- **Range**: The function starts from a minimum \(y\) value of \(-3\) and increases, so the range can be expressed as:
  \[
  y \geq -3
  \]

### Final Answer:
- **Domain**: \(x \geq -3\)
- **Range**: \(y \geq -3\)

If you need further details or have any questions, feel free to ask!

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Here are some related questions to expand on this topic:
1. What is the difference between the domain and range of a function?
2. How would the inequalities change if the graph included negative infinity for the range?
3. Can you explain how to find the domain and range of other common functions like \(x^2\)?
4. What impact does shifting the graph up or down have on the range inequality?
5. How would the domain and range change if the graph were reflected over the x-axis?

**Tip**: Always check for restrictions in the domain, such as divisions by zero or square roots of negative numbers, when determining inequalities.

Learn how to write domain and range as inequalities for a function graph. This solution provides step-by-step analysis of the graph, identifying the domain and range based on visual inspection. Suitable for high school students and anyone interested in understanding function graphs and inequalities.

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