On a coordinate plane, a straight red line with a negative slope, labeled g of x, crosses the y-axis at (0, negative 7). A straight blue line with a positive slope, labeled f of x, crosses the x-axis at (negative 1, 0) and the y-axis at (0, 2). Both lines intersect at (negative 3, negative 4).

Question

Which statement is true regarding the functions on the graph?

f(–3) = g(–4)
f(–4) = g(–3)
f(–3) = g(–3)
f(–4) = g(–4)

Answer 1

Given the information:

- The red line \( g(x) \) crosses the y-axis at \( (0, -7) \) and has a negative slope.
- The blue line \( f(x) \) crosses the x-axis at \( (-1, 0) \) and the y-axis at \( (0, 2) \) and has a positive slope.
- Both lines intersect at \( (-3, -4) \).

We want to determine which statement among the following is true:

1. \( f(-3) = g(-4) \)
2. \( f(-4) = g(-3) \)
3. \( f(-3) = g(-3) \)
4. \( f(-4) = g(-4) \)

From the given conditions, observe the point of intersection:
- The functions \( f(x) \) and \( g(x) \) intersect at \( (-3, -4) \).

Thus, at \( x = -3 \):
- \( f(-3) = -4 \)
- \( g(-3) = -4 \)

This leads us to the equation \( f(-3) = g(-3) \) because both functions have the same output at the x-coordinate where they intersect.

Therefore, the true statement is:

\[ f(-3) = g(-3) \]

So, the correct answer is:

\[ f(-3) = g(-3) \]