https://file.aiquickdraw.com/mathbot/file/1730235004581k90dxuqb.jpg

Let's examine each statement based on the graph:

1. **\( f(0) > g(0) \):**  
   At \( x = 0 \), we need to compare the values of \( f \) and \( g \). From the graph, \( f(0) = 0 \) (since it intersects the origin), and \( g(0) \approx 15 \). Therefore, \( f(0) < g(0) \), so this statement is **false**.

2. **There are two values of \( x \) where \( f(x) = g(x) \):**  
   By inspecting the intersections, \( f \) and \( g \) intersect at two points: one around \( x \approx -2 \) and another around \( x \approx 2 \). So, this statement is **true**.

3. **If \( g(x) = 15 \), then \( x = 1 \):**  
   Checking where \( g(x) = 15 \), we observe that this occurs at both \( x = 1 \) and \( x = 3 \). Thus, the statement "If \( g(x) = 15 \), then \( x = 1 \)" is incomplete, as there’s another value where \( g(x) = 15 \). This statement is **false**.

4. **\( f(-3) > g(4) \):**  
   At \( x = -3 \), \( f(-3) \approx 15 \), and at \( x = 4 \), \( g(4) = 0 \). Therefore, \( f(-3) > g(4) \), making this statement **true**.

### Conclusion:
The correct statements are:
- **There are two values of \( x \) where \( f(x) = g(x) \)**
- **\( f(-3) > g(4) \)**

Would you like more detailed explanations for each step?

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Here are 5 related questions to deepen understanding:
1. What does it mean when two functions intersect at certain points on a graph?
2. How can you determine function values at specific points without an equation?
3. Why is the inequality \( f(0) > g(0) \) false in this case?
4. What method can be used to find all \( x \)-values where \( f(x) = g(x) \)?
5. How would the answer change if \( f(x) \) and \( g(x) \) were altered?

**Tip:** When comparing function values, focus on the y-values at specific x-values for quick assessments.

Here are two graphs representing functions f and g. Select all statements that are true about functions f and g:
- f(0) > g(0)
- There are two values of x where f(x) = g(x)
- If g(x) = 15, then x = 1
- f(-3) > g(4)

Learn how to interpret function graphs and evaluate statements about functions f and g based on their intersections and values at specific points. Ideal for students in Grades 8-10, this problem enhances understanding of function comparison and graph analysis.

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