Problem
Select all of the transformations that have occurred to the function $f(x)=\log (-x)+4$ as compared to the parent function, $f(x)=\log x$. reflect over the y axis reflect over the $x$ axis reflect over the line $y=k$ reflect over the line $x=h$ up 4 units down 4 units left 4 units right 4 units
Solution
Step 1 ：The function $f(x)=\log (-x)+4$ is compared to the parent function $f(x)=\log x$ to identify the transformations.
Step 2 ：The negative sign in front of $x$ in the function $f(x)=\log (-x)+4$ indicates a reflection over the y-axis.
Step 3 ：The addition of 4 to the function $f(x)=\log (-x)+4$ indicates a vertical shift up by 4 units.
Step 4 ：\(\boxed{\text{The transformations that have occurred are: reflection over the y axis and up 4 units.}}\)
