Respuesta :
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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domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Answer:
Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
Step-by-step explanation:
Given : [tex]h(x)=(0.5)^x-9[/tex]
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 [tex]h(x)=(0.5)^x-9[/tex] is an exponential function
So, the domain of the function is,
[tex]D=(-\infty,\infty) , x|x\in \mathbb{R}[/tex]
i.e, The set of all real numbers.
Range is the set of value that corresponds to the domain.
Let [tex]y=(0.5)^x-9[/tex]
If [tex]x\rightarrow \infty , y\rightarrow -9[/tex]
If [tex]x\rightarrow -\infty , y\rightarrow \infty[/tex]
So, The range of the function is
[tex]R=(-9,\infty) , y|y>-9[/tex]
The asymptote of the function,
Exponential functions have a horizontal asymptote.
The equation of the horizontal asymptote is when
[tex]x\rightarrow \infty[/tex]
[tex]y=(0.5)^\infty-9[/tex]
[tex]y=-9[/tex]
Therefore, Option 4 is correct.
Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
