Answer
False
Work Step by Step
$g(x) = f(x-k)$, where $k$ is a constant, would shift the graph of $f$ to the left or right, making the critical numbers of $g$ different than those of $f$.
Example: $f(x)=\frac{1}{x}$
Critical number: $0$
$g(x)=\frac{1}{x-7}$
Critical number: $7$
The given statement is false.
