What is the minimum value of f(x) = |x + 4| - 3?

The graph of $|x+4|$ is a V shape whose lowest point is where the expression inside the bars is zero, at $x=-4$. At that point $f(-4)=|0|-3=-3$. The absolute value part is never negative, so the smallest possible value of $f$ is $0-3=-3$, choice J. Choice F ($-4$) is the $x$-coordinate where the minimum occurs, not the minimum value. Choice H ($3$) and choice G ($4$) come from sign errors in reading the shifts. The question asks for the minimum value of the function, which is an output, so read the vertical shift, $-3$.