Step-by-step explanation
In general, a vertically compression of a function f(x) is obtained by the transformation:
![f(x)\rightarrow g(x)=(1)/(k)\cdot f(x).](https://img.qammunity.org/2023/formulas/mathematics/college/xaa0bh3otubv16pv87ucghrbst8nug4mwb.png)
Where k > 1 is the factor of compression.
In this case we have f(x) = |x| and k = 4. Applying the transformation above, we get:
![g(x)=(1)/(4)\cdot|x|.](https://img.qammunity.org/2023/formulas/mathematics/college/ruf1lcopycf7zqhu7l7l508dyn06tpoy1s.png)
Answer
C.
![g(x)=(1)/(4)|x|](https://img.qammunity.org/2023/formulas/mathematics/college/p9bg0nmncz7ccsmb24xdx4z98t57g31t79.png)