The equation for the function graphed is: f(x) = (x - 3) / ((x + 1)(x - 4))
Piecewise function: The graph exhibits two linear pieces with different slopes, indicating a piecewise function.
Slopes and intercepts: We can identify the slopes and y-intercepts of each piece from the graph.
Asymptotes: The vertical asymptotes at x = -1 and 4 correspond to the zeros of the denominator, suggesting the form of the function.
Horizontal asymptote: The horizontal asymptote at y = 0 confirms the overall behavior of the function.
Intercept at x = 3: The point of intersection between the two pieces occurs at x = 3, which helps refine the function further.
Considering all these observations, the function with the equation f(x) = (x - 3) / ((x + 1)(x - 4)) perfectly matches the given graph. It exhibits the desired slopes, intercepts, and asymptotes.