Example: Find the horizontal asymptote of the function:
\[ g(x) = 13(2-4^{-x}) \]Solution
This is most easily accomplished by simplifying the expression: \[g(x) = 26-13\cdot 4^{-x}\]Given that there is a vertical shift by +26, this function must have transformed the horizontal asymptote up by 26 units. Hence, the horizontal asymptote must be 26. A quick visual inspection of the graph validates this: