The discussion focuses on finding the equation for the horizontal asymptote of the exponential function $$g(x) = -2f(2x - 6)$$, where $$f(x) = 4^x$$. The horizontal asymptote of the function $$f(x)$$ is established as $$y = 0$$ since exponential functions approach zero as $$x$$ approaches negative infinity. Consequently, the transformation applied in $$g(x)$$ does not affect the horizontal asymptote, which remains at $$y = 0$$.
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