Question

Which statement is true regarding the graphed functions?

On a coordinate plane, a red curved line with an upward arc, labeled g of x, crosses the x-axis at (negative 2, 0), and the y-axis at (0, 4). A blue curved line with an upward arc, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).

f(0) = g(0)
f(–2) = g(–2)
f(0) = g(–2)
f(–2) = g(0)

Answer 1

To analyze the functions \( f(x) \) and \( g(x) \) based on the provided graph descriptions, we can identify the following key points:

1. For \( g(x) \):
- \( g(-2) = 0 \) (since it crosses the x-axis at \( (-2, 0) \))
- \( g(0) = 4 \) (since it crosses the y-axis at \( (0, 4) \))

2. For \( f(x) \):
- \( f(0) = 4 \) (since it crosses the y-axis at \( (0, 4) \))
- \( f(2) = 0 \) (since it crosses the x-axis at \( (2, 0) \))

Now we can evaluate the given statements:

- **Statement 1**: \( f(0) = g(0) \)
- \( f(0) = 4 \) and \( g(0) = 4 \) → This statement is **true**.

- **Statement 2**: \( f(-2) = g(-2) \)
- We do not have information about \( f(-2) \), but we know \( g(-2) = 0 \). Without specific information about \( f(-2) \), we cannot confirm this statement.

- **Statement 3**: \( f(0) = g(-2) \)
- \( f(0) = 4 \) and \( g(-2) = 0 \) → This statement is **false**.

- **Statement 4**: \( f(-2) = g(0) \)
- We do not know \( f(-2) \), but we know \( g(0) = 4\). Therefore, we cannot confirm this statement.

The only statement that is definitively true based on the given information is:

**f(0) = g(0)**.