Final answer:
For f(x) = (1/2)^x, the graph is an exponential decay curve with a horizontal asymptote at the x-axis. The domain is all real numbers, and the range is all positive real numbers above zero.
Step-by-step explanation:
For the function f(x) = (1/2)^x, we are interested in the graph, asymptote, domain, and range of the function.
The graph of this function is an exponential decay curve because the base of the exponent, (1/2), is between 0 and 1. As x increases, the value of f(x) decreases towards 0, but never actually reaches it, which means the x-axis is a horizontal asymptote. The domain of this function is all real numbers, because you can raise (1/2) to any power. Hence, the domain is (-∞, ∞).
The range of the function is all positive real numbers, as the output of the function never reaches or goes below zero, but it can approach zero infinitely close. Thus, the range is (0, ∞).
To draw the graph, we would label it with f(x) and x, use a continuous curve that approaches the x-axis as x increases, and scale the axes accordingly.