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).

Question

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:

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