MHB Equation for the horizontal asymptote.

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To find the horizontal asymptote of the function g(x) = -2f(2x - 6), where f(x) = 4^x, one must first identify the horizontal asymptote of f(x). The function f(x) approaches 0 as x approaches negative infinity, indicating that its horizontal asymptote is y = 0. Since g(x) is a transformation of f(x), the horizontal asymptote remains unchanged by vertical shifts or reflections. Therefore, the horizontal asymptote for g(x) is also y = 0. Understanding the behavior of exponential functions is key to determining their asymptotic properties.
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How would you find the equation for the horizontal asymptote of the following exponential function?:
$$g(x) = -2f(2x - 6)$$

Let $$f(x) = 4^x$$
 
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I would begin by looking at the horizontal asymptote of $f$...can you see what this is?
 

Thread 'Area of Overlapping Squares'

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