Respuesta :
Considering it's horizontal asymptote, the statement describes a key feature of function g(x) = 2f(x) is given by:
Horizontal asymptote at y = 0.
What are the horizontal asymptotes of a function?
They are the limits of the function as x goes to negative and positive infinity, as long as these values are not infinity.
Researching this problem on the internet, the functions are given as follows:
- [tex]f(x) = 2^x[/tex].
- [tex]g(x) = 2f(x) = 2(2)^x[/tex]
The limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 2(2)^x = \frac{2}{2^{\infty}} = 0[/tex]
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 2(2)^x = 2(2)^{\infty} = \infty[/tex]
Hence, the correct statement is:
Horizontal asymptote at y = 0.
More can be learned about horizontal asymptotes at https://brainly.com/question/16948935
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