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.