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.