The transformation \( f(x) \mapsto f(x+1) \) translates the graph of the function \( f(x) \) 1 unit to the left.
Here's why:
- The expression \( f(x + 1) \) implies that for each \( x \) value on the original graph, the output corresponds to the input \( x+1 \). This means to get the same output as \( f(x) \) at point \( x \), you need to input \( x+1 \).
- Therefore, in order to map the output of \( f(x) \) to a value that is at the original position, we must move the point where it's being evaluated by one unit to the left.
So the correct answer is: translates it 1 unit left and 1 unit up.