Which expression represents translating f(x) to the left by 4 units?

Which expression represents translating f(x) to the left by 4 units?

• A. g(x) = f(x - 4)
• B. g(x) = f(x + 4)
• C. g(x) = f(x) - 4
• D. g(x) = f(-x) + 4

Answer: (B)

Horizontal shifts come from the sign inside the function’s argument. If you replace x with x − h, the graph moves to the right by h; if you replace x with x + h, it moves to the left by h. To move f(x) left by 4 units, you use x + 4 inside, giving g(x) = f(x + 4). The other forms do something different: f(x) − 4 shifts the graph down 4 units, f(−x) reflects the graph across the y-axis, and f(−x) + 4 would reflect and then move up, not shift left.

Horizontal shifts come from the sign inside the function’s argument. If you replace x with x − h, the graph moves to the right by h; if you replace x with x + h, it moves to the left by h. To move f(x) left by 4 units, you use x + 4 inside, giving g(x) = f(x + 4). The other forms do something different: f(x) − 4 shifts the graph down 4 units, f(−x) reflects the graph across the y-axis, and f(−x) + 4 would reflect and then move up, not shift left.