Question

Which function's graph is a translation of the graph f(x) = x shifted 5 units to the right?

A. f(x) = x + 5
B. f(x) = x - 5
C. f(x) = x + 5
D. f(x) = x - 5

Answer 1

The function representing the graph of f(x) = x shifted 5 units to the right is B. f(x) = x - 5, based on the algebraic principle of horizontal translations.

Step-by-step explanation:

The graph of the function f(x) = x shifted 5 units to the right would be represented by the function f(x) = x - 5. To understand this, recall that for any function f(x), the function f(x - d) translates the graph d units to the right along the x-axis. Therefore, if the original function is f(x) = x, then shifting it 5 units to the right would be done by substituting x with x - 5, giving us f(x - 5), which simplifies to f(x) = x - 5. Hence, the correct answer is B. f(x) = x - 5.