Question

when x is very large, the graph of y=(1/2)^x approaches the x-axis. that is, as x gets larger and larger (farther to the right along the curve), the closer the curve gets to the x-axis. in this situation, the x-axis is called an asymptote of y=(1/2)^x. does function y=(1/2)^x have a vertical asymptote? in other words, is there a vertical line that the graph above approaches? why or why not

Answer 1

No, the function y=(1/2)^x does not have a vertical asymptote. A vertical asymptote occurs when the function approaches infinity or negative infinity as x approaches a certain value, but this is not the case for y=(1/2)^x. As x approaches infinity, the value of y approaches zero, but there is no specific x-value where the function "blows up" to infinity or negative infinity. Therefore, the function does not have a vertical asymptote.