If a function g(x) is transformed by shifting left by 4, what is the new expression?

If a function g(x) is transformed by shifting left by 4, what is the new expression?

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

Answer: (D)

Shifting a graph horizontally is done by changing the input to the function. To move the graph left by 4 units, you replace x with x + 4. That gives the transformed function y = g(x + 4). Intuitively, every point (a, g(a)) on the original graph appears four units to the left as (a − 4, g(a)) on the new graph, since plugging x = a − 4 into g(x + 4) yields g((a − 4) + 4) = g(a). The other forms would do different things: g(x) + 4 lifts the graph up by 4 units, not shift it horizontally; g(x − 4) moves the graph to the right by 4 units; g(x) − 4 moves it down by 4 units.

Shifting a graph horizontally is done by changing the input to the function. To move the graph left by 4 units, you replace x with x + 4. That gives the transformed function y = g(x + 4). Intuitively, every point (a, g(a)) on the original graph appears four units to the left as (a − 4, g(a)) on the new graph, since plugging x = a − 4 into g(x + 4) yields g((a − 4) + 4) = g(a).

The other forms would do different things: g(x) + 4 lifts the graph up by 4 units, not shift it horizontally; g(x − 4) moves the graph to the right by 4 units; g(x) − 4 moves it down by 4 units.