The fourth option is correct because [tex]g(x)=2\cdot 8^x[/tex].
Given:
The given function is:
[tex]f(x)=8^x[/tex]
To find:
The function that represents a transformation of [tex]f(x)[/tex] by a vertical stretch with factor [tex]2[/tex].
Explanation:
If a function [tex]f(x)[/tex] is vertically stretched by factor [tex]k[/tex], then
[tex]g(x)=k\cdot f(x)[/tex]
It is given that the function [tex]f(x)[/tex] is vertically stretched by factor [tex]2[/tex]. So,
[tex]g(x)=2\cdot f(x)[/tex]
[tex]g(x)=2\cdot 8^x[/tex]
Therefore, the fourth option is correct.
Learn more:
https://brainly.com/question/12031230
