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

Question

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

in progress 0

The domain of h(x) is {x : x is a real number}

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

The horizontal asymptote is at y = -9

The domain of h(x) is {x : x u2208 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

u2235 h(x) = (0.5)^x – 9

u2235 All the values of x make h(x) defined

u2235 The domain of the function is the values of x

u2234 The domain of h(x) is {x : x u2208 R} u21d2 R is the set of real number

u2235 The range of the function is the set of values of y which

corresponding to x

u2235 (0.5)^x must be positive because there is no values of x make it

negative value

u2234 y must be greater than -9

u2234 The range of the function is {y : y > -9}

u2235 A function of the form f(x) = a (bx) + c always has a horizontal

asymptote at y = c

u2235 h(x) = (0.5)^x – 9

u2234 c = -9

u2234 The horizontal asymptote is at y = -9

* Look to the attached file for more understanding