The equation for g(x) is g(x) = 3x - 2 based on the given characteristics of the graph.
The graph of g(x) appears to be a transformation of the graph of f(x) = 3x. Given the characteristics described, let's deduce the equation for g(x).
1. Shift in the y-direction:
The graph starts at (-5, -2) and ends at (5, y), indicating a vertical shift. Let's consider the form g(x) = 3x + c.
2. Passes through the points (-1, -1) and (0, 1):
Substituting these points into the equation:
g(-1) = 3(-1) + c = -1
g(0) = 3(0) + c = 1
Solving these equations gives c = -2.
3. Ending at (5, y):
Substituting x = 5 into the equation:
g(5) = 3(5) - 2 = 13
Therefore, the equation for g(x) is g(x) = 3x - 2 based on the given characteristics of the graph.