The graph of $f(x) = |x| + 2$ is the graph of $y = |x|$ shifted in which direction?

Adding a positive constant to a function shifts its graph upward. So $|x| + 2$ shifts $y = |x|$ upward by 2 units, lifting the V-shape's vertex from the origin to $(0, 2)$. Subtracting a constant would shift downward; modifying the input inside $|\cdot|$ shifts left or right.