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

The domain of h(x) is {x : x ∈ R}

The range of the function is {y : y > -9}

The horizontal asymptote is at y = -9

Step-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