https://file.aiquickdraw.com/mathbot/file/17260781576008a9bo702.jpg

Looking at the graph, we have two functions: \( f(x) \) (in blue) and \( g(x) \) (in red). Let's analyze the given points from the graph to check which statement is true.

### Step 1: Find the value of \( f(0) \) and \( g(-2) \)
- From the graph, at \( x = 0 \):
  - \( f(0) = 4 \) (the blue curve is at 4 when \( x = 0 \))
  - \( g(0) = 0 \) (the red curve crosses the x-axis at 0)
  
- Now for \( g(-2) \):
  - \( g(-2) = 4 \) (the red curve reaches a value of 4 when \( x = -2 \))

### Step 2: Check each option
- **Option 1:** \( f(0) = 2 \) and \( g(-2) = 0 \)
  - Incorrect. \( f(0) = 4 \), not 2.

- **Option 2:** \( f(0) = 4 \) and \( g(-2) = 4 \)
  - Correct! This matches the values from the graph.

- **Option 3:** \( f(-2) = 0 \) and \( g(-2) = 0 \)
  - Incorrect. \( g(-2) = 4 \), not 0.

- **Option 4:** \( f(4) = 4 \) and \( g(-4) = 4 \)
  - Incorrect. \( f(4) \) does not exist on the graph and \( g(-4) \) is not 4.

### Conclusion:
The correct statement is **Option 2**: \( f(0) = 4 \) and \( g(-2) = 4 \).

Do you need further details or have any questions?

### Relative Questions:
1. How do you find the values of functions from a graph?
2. Can you explain why \( g(x) = 0 \) at certain points?
3. What does it mean for a function to cross the x-axis?
4. How do quadratic functions typically behave based on their graphs?
5. Can you derive the equations for \( f(x) \) and \( g(x) \) from this graph?

### Tip:
Always check the behavior of both functions at key points like \( x = 0 \) and the intercepts for better understanding.

Which statement is true regarding the graphed functions?

Learn how to analyze quadratic functions from a graph by comparing function values at specific points. This problem involves function evaluation, graph interpretation, and the behavior of quadratic functions. Suitable for students in Grades 9-10.

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