https://file.aiquickdraw.com/mathbot/file/17259249563837kwxv0iu.jpg

Let's first analyze the graph in the image and solve the problems step by step.

### Question 1: Solve the following equations using the graph of \( f(x) \)

1. \( f(x) = 0 \)
   - Look for where the graph intersects the x-axis (i.e., where \( y = 0 \)).
   - From the graph, it intersects the x-axis at \( x = -3 \) and \( x = 3 \).
   - **Answer:** \( x = -3, 3 \)

2. \( f(x) = 3 \)
   - Check where the value of the graph is 3 (i.e., where the graph reaches \( y = 3 \)).
   - From the graph, there is no point where \( f(x) = 3 \). 
   - **Answer:** DNE (Does Not Exist)

3. \( f(x) = -10 \)
   - Look for where the graph reaches \( y = -10 \).
   - This happens at \( x = 6 \) (solid dot indicates it is included).
   - **Answer:** \( x = 6 \)

4. \( f(x) = 5 \)
   - Check where the graph reaches \( y = 5 \).
   - The graph does not reach \( y = 5 \) at any point.
   - **Answer:** DNE (Does Not Exist)

### Question 2: Solve the inequalities using the graph of \( f(x) \)

1. \( f(x) \geq 0 \)
   - Find where the graph is above or touching the x-axis (i.e., \( y \geq 0 \)).
   - From the graph, this occurs from \( x = -3 \) to \( x = 3 \), both inclusive.
   - **Answer:** \( [-3, 3] \)

2. \( f(x) < -10 \)
   - Check where the graph is below \( y = -10 \).
   - The graph never goes below \( y = -10 \).
   - **Answer:** DNE (Does Not Exist)

Would you like further details or clarifications? Let me know!

Here are 5 related questions that could help you expand your understanding:
1. How do we determine where a graph crosses the x-axis?
2. What is the significance of open circles on a graph?
3. How can inequalities be interpreted from a graph?
4. How do you determine intervals where the graph is positive or negative?
5. What does it mean if a solution does not exist for a particular equation?

**Tip:** When analyzing graphs, pay close attention to open and closed circles. Open circles mean the point is not included in the graph, while closed circles mean the point is part of the graph.

Use the graph to solve the equations and inequalities based on the function f(x).

Learn how to solve equations and inequalities using the graph of a function. This problem involves finding where f(x) equals specific values and determining intervals of inequality. Suitable for high school students.

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