https://file.aiquickdraw.com/mathbot/file/172609880791416n3a8ni.jpg

Based on the question provided in the image, the function \( y = F(x) \) is defined such that when \( x = -3 \), its \( y \)-value is 0, or in function terms, \( F(-3) = 0 \).

Let's go through the options one by one to find the correct answers:

- **A. \( F(-3) = 0 \)**  
  This is directly true because the problem states that the y-value is 0 when \( x = -3 \).

- **B. The point \( (0, -3) \) is on the graph of the function.**  
  This is false because the point \( (0, -3) \) would imply that when \( x = 0 \), \( y = -3 \). There is no information in the problem suggesting this relationship.

- **C. The point \( (-3, 0) \) is on the graph of the function.**  
  This is true because \( F(-3) = 0 \), which corresponds to the point \( (-3, 0) \).

- **D. The function's value is \( -3 \) at \( 0 \).**  
  This is false because there is no information given that \( F(0) = -3 \).

- **E. The function's value is \( 0 \) at \( -3 \).**  
  This is true since \( F(-3) = 0 \) as explicitly stated in the problem.

- **F. \( F(0) = -3 \)**  
  This is false because no information is provided that confirms this statement.

### Correct answers:  
- A  
- C  
- E

Would you like a detailed explanation of any specific part?  
Here are 5 related questions to explore further:
1. What is the graphical interpretation of a function's point?
2. How do you determine if a point is on the graph of a function?
3. Can a function have multiple outputs for the same input?
4. How would the graph change if the function value at \( F(0) \) were given as 1 instead of \( -3 \)?
5. What are the implications if \( F(-3) \) were not equal to zero?

**Tip:** Always plot function points to visually verify their positions on the graph!

For the function y = F(x), when x = -3, its y-value is 0. Choose all true statements.

In this problem, learn how to evaluate a function at a given x-value, specifically when F(x) = 0 at x = -3. Explore points on the graph and true statements for the function. Ideal for students in Grades 8-10.

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