What are the domain range and asymptote of h(x) (0.5)x 9?

The function ( h(x) = (0.5)^x + 9 ) has a domain of all real numbers, ( (-\infty, \infty) ), because exponential functions are defined for every real input. The range is ( (9, \infty) ) since ( (0.5)^x ) approaches 0 as ( x ) approaches infinity, making the minimum value of ( h(x) ) equal to 9. The horizontal asymptote is ( y = 9 ), as the function approaches this value but never actually reaches it.