What are the domain, range, and asymptote of h(x) = (0.5)x - 9

Answer:The domain of h(x) is {x : x ∈ R}The range of the function is {y : y > -9}The horizontal asymptote is at y = -9Step-by-step explanation:* Lets read the problem and solve it- The exponential function is f(x) = a(b)^x, where a and b are constant   and b is the base , x is the exponent , a is the initial value of f(x)- The domain of the function is all the values of x which make the   function defined- The range of the function is the set of values of y that corresponding   with the domain x- Asymptote on the graph a line which is approached by a curve but  never reached- A function of the form f(x) = a(b^x) + c always has a horizontal  asymptote at y = c* Lets solve the problem∵ h(x) = (0.5)^x - 9 ∵ All the values of x make h(x) defined∵ The domain of the function is the values of x∴ The domain of h(x) is {x : x ∈ R} ⇒ R is the set of real number∵ The range of the function is the set of values of y which    corresponding to x∵ (0.5)^x must be positive because there is no values of x make it   negative value∴ y must be greater than -9∴ The range of the function is {y : y > -9}∵ A function of the form f(x) = a (bx) + c always has a horizontal    asymptote at y = c∵ h(x) = (0.5)^x - 9∴ c = -9∴ The horizontal asymptote is at y = -9* Look to the attached file for more understanding