The graph of $f(x) = \frac{3}{x-1} + 2$ is shown, The graph of $f(x)$ was transformed to get the graph of $g(x)$ as shown - HSC - SSCE Mathematics Extension 1 - Question 2 - 2022 - Paper 1

To understand the transformation that was applied to the function $f(x)$, we first analyze the original function:

$f(x) = \frac{3}{x-1} + 2$

This function has a vertical asymptote at $x = 1$ (since the denominator becomes zero), and its range is affected by the constant $2$, which shifts the graph upwards.

Now, examining the transformed function $g(x)$, we must determine the nature of the transformation.

After observing the behavior of the graph of $g(x)$, the transformation can be seen as reflecting the graph of $f(x)$ across the $y$-axis, which corresponds to plugging in $|x|$. Therefore, the appropriate transformation applied is:

$g(x) = f(|x|)$

Thus, the correct answer is option A.