https://file.aiquickdraw.com/mathbot/file/1728935011527d1mjh73o.jpg

Let's analyze the given graph and answer each question based on its characteristics:

1. **Domain of the Function**:
   The graph extends infinitely in both the left and right directions (as indicated by the arrows), meaning the function covers all possible \( x \)-values. 
   - **Answer**: \( (-\infty, \infty) \)

2. **Range of the Function**:
   The graph reaches its highest point at \( y = 6 \) and extends downward infinitely. Thus, the range covers all \( y \)-values from negative infinity up to 6.
   - **Answer**: \( (-\infty, 6] \)

3. **Intervals of Increase**:
   The function increases from the left up to the peak at \( x = -3 \). Hence, the increasing interval is from \( -\infty \) to \( -3 \).
   - **Answer**: \( (-\infty, -3] \)

4. **Intervals Where \( f(x) \geq 0 \)**:
   The function is above or equal to the \( x \)-axis (where \( y \geq 0 \)) between \( x = -5 \) and \( x = 1 \).
   - **Answer**: \( [-5, 1] \)

Let me know if you would like further explanations or have any more questions!

Here are five related questions to deepen understanding:
1. How would the domain change if the graph had a break at \( x = 0 \)?
2. What would the range be if the highest point of the graph was at \( y = 10 \)?
3. How can you determine the intervals of decrease from the graph?
4. If the graph had no arrows, what would the domain and range be?
5. How do you determine if a function is increasing or decreasing on a graph?

**Tip**: When identifying the domain and range of a function from a graph, always consider any arrows indicating that the function extends infinitely.

Determine the domain, range, intervals of increase, and intervals where the function f(x) is greater than or equal to zero based on the graph provided.

Learn how to find the domain, range, intervals of increase, and intervals where a function is non-negative from its graph. This exercise involves understanding key mathematical concepts like graph analysis and function properties. Suitable for students in Grades 9-11.

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