Question

On a coordinate plane, a red line, labeled g of x, begins on a negative slope, crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and crosses the x-axis on a positive slope at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 2) and the x-axis at (2, 0).
Which statement is true regarding the functions on the graph?

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

Answer 1

To determine which statements are true regarding the functions \( f(x) \) and \( g(x) \), we will evaluate the given points based on the descriptions of the lines.

1. **For \( f(x) \)**:
- The blue line crosses the y-axis at \( (0, 2) \), hence \( f(0) = 2 \).
- The blue line crosses the x-axis at \( (2, 0) \), hence \( f(2) = 0 \).

2. **For \( g(x) \)**:
- The red line crosses the y-axis at \( (0, -2) \), hence \( g(0) = -2 \).
- The red line crosses the x-axis at \( (2, 0) \), hence \( g(2) = 0 \).

Now we can evaluate each statement:

1. **\( f(2) = g(2) \)**:
- \( f(2) = 0 \) and \( g(2) = 0 \).
- **True**.

2. **\( f(0) = g(0) \)**:
- \( f(0) = 2 \) and \( g(0) = -2 \).
- **False**.

3. **\( f(2) = g(0) \)**:
- \( f(2) = 0 \) and \( g(0) = -2 \).
- **False**.

4. **\( f(0) = g(2) \)**:
- \( f(0) = 2 \) and \( g(2) = 0 \).
- **False**.

Based on these evaluations, the only true statement is:

**\( f(2) = g(2) \)**.