Select the correct answer. What is the equation of the asymptote for this function? f(x)=((1)/(2))^x+3 A. x=0 B. y=0 C. x=3 D. y=3

To determine the equation of the asymptote for the function \( f(x) = \left(\frac{1}{2}\right)^x + 3 \), we need to analyze the behavior of the function as \( x \) approaches positive or negative infinity.<br /><br />The function \( f(x) = \left(\frac{1}{2}\right)^x + 3 \) is an exponential function. As \( x \to \infty \), the term \( \left(\frac{1}{2}\right)^x \) approaches 0 because any number less than 1 raised to a large power approaches 0. Therefore, the function approaches:<br /><br />\[ f(x) \approx 0 + 3 = 3 \]<br /><br />This indicates that the horizontal asymptote of the function is \( y = 3 \).<br /><br />Therefore, the correct answer is:<br /><br />D. \( y = 3 \)