Question

what is the equation of the horizontal asymptote of the graph for the following function? $f(x) = 2^{x - 2} + 9$ a $y = 0$ b $y = 2$ c $y = 9$ d $y = -2$

Explanation:

Step1: Analyze exponential term behavior

As $x \to \pm\infty$, $2^{x-2} \to 0$

Step2: Find limit of $f(x)$

$\lim_{x \to \pm\infty} f(x) = \lim_{x \to \pm\infty} (2^{x-2} + 9) = 0 + 9 = 9$

Answer:

C. $y=9$