
The function f(x) is a non-linear mapping of input values to negative output values. The function has a local minimum around the input of -64.

[DOMAIN]:
The domain of the function is [-128, 128]. The interval with unexpected behavior is between -80 and -48, where the function reaches its minimum value.

[CODE]:
def approximate_function(x):
    import math
    return -1 * (1 + math.exp(-0.025 * (x + 64))) + (-6.25 * math.exp(-((x + 64) ** 2) / 500))

Please note that this is an approximation of the function, and the actual behavior might be slightly different.