Final answer:
The function f(x) = x shifted up by 1 unit and to the left by 2 units is represented by the option B. f(x + 2) + 1.
Step-by-step explanation:
When dealing with transformations of functions, it is important to understand how to shift graphs vertically and horizontally. Specifically, if we have a function f(x), shifting this graph up by a certain amount will result in adding that amount to the function. On the other hand, a horizontal shift to the left or right involves adding or subtracting a value inside the function argument.
For the function f(x) = x, being shifted up 1 unit will add 1 to the entire function, resulting in f(x) + 1. Shifting the graph to the left by 2 units involves subtracting 2 from the x value within the function. This is because moving to the left on the x-axis implies a reduction in the x value. The function then becomes f(x+2). Combining both these transformations will give us the final shifted function:
The correct option, which represents the function f(x) shifted up 1 unit and to the left 2 units, is B. f(x + 2) + 1.