We are asked to identify a function that has been vertically stretched. A function being vertically stretched means that the absolute value of the factor must be greater than zero. Here, we can see that the first option clearly doesn't work, as the absolute value of [tex] \frac{1}{4} \ \textless \ 0[/tex]. Moving on to the second option, we can see that the factor is [tex]4[/tex]. Since [tex]4\ \textgreater \ 0[/tex], this function indicates a vertical stretch. Therefore, the radical function that contains a vertical stretch is [tex]\boxed{f(x)=4 \sqrt{x-2}}[/tex]. However, you might be wondering about the third and fourth function. They aren't applicable because they don't contain a factor on the 'outside' of the radical function, meaning that the function does not even contain a vertical stretch or shrink. Hope this helped and have a great day!
