What is the horizontal asymptote of the function \( y = \left(\frac{1}{2}\right)^x + 2 \)?
Answer (2)
x → − ∞ lim ( 2 1 ) x + 2 = ∞ + 2 = ∞ x → ∞ lim ( 2 1 ) x + 2 = 0 + 2 = 2
There is one-sided horizontal asymptote y = 2
The horizontal asymptote of the function y = ( 2 1 ) x + 2 is y = 2 as x → + ∞ . As x approaches negative infinity, the function increases without bound. Thus, the asymptote demonstrates the behavior of the function in the positive domain.
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