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

Answer

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Answer

$The transformations that have occurred are: reflection over the y axis and up 4 units.$

Steps

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 ： $The transformations that have occurred are: reflection over the y axis and up 4 units.$