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

domain: {x | x > 9}; range: {y | y is a real number}; asymptote: y = 9

domain: {x | x > –9}; range: {y | y is a real number}; asymptote: y = –9

domain: {x | x is a real number}; range: {y | y > 9}; asymptote: y = 9

domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Among the choices provided above the domain, range, and asymptote of h(x) = (0.5)x – 9 is the below:

domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

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tardymanchester tardymanchester · Answer 2 · 2019-03-08T00:51:19-05:00

Answer:

Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Step-by-step explanation:

Given : \(h(x)=(0.5)^x-9\)

To find : What are the domain, range, and asymptote of h(x) ?

Solution :

Domain of the function is where the function is defined

The given function \(h(x)=(0.5)^x-9\) is an exponential function

So, the domain of the function is,

\(D=(-\infty,\infty) , x|x\in \mathbb{R}\)

i.e, The set of all real numbers.

Range is the set of value that corresponds to the domain.

Let \(y=(0.5)^x-9\)

If \(x\rightarrow \infty , y\rightarrow -9\)

If \(x\rightarrow -\infty , y\rightarrow \infty\)

So, The range of the function is

\(R=(-9,\infty) , y|y>-9\)

The asymptote of the function,

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is when

\(x\rightarrow \infty\)

\(y=(0.5)^\infty-9\)

\(y=-9\)

Therefore, Option 4 is correct.

Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9