Which expression represents translating the graph of f(x) to the left by h units?

Which expression represents translating the graph of f(x) to the left by h units?

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

Answer: (A)

Moving a graph left or right is done by changing the input to the function. To shift f(x) to the left by h units, replace x with x + h, giving g(x) = f(x + h). Reasoning: a point on the original graph at (a, f(a)) becomes a point on the new graph at (a − h, g(a − h)) = (a − h, f(a)), which is exactly h units to the left. If you used g(x) = f(x − h), the shift would be to the right. Shifting the output, as in f(x) + h or f(x) − h, only moves the graph up or down, not horizontally.

Moving a graph left or right is done by changing the input to the function. To shift f(x) to the left by h units, replace x with x + h, giving g(x) = f(x + h).

Reasoning: a point on the original graph at (a, f(a)) becomes a point on the new graph at (a − h, g(a − h)) = (a − h, f(a)), which is exactly h units to the left. If you used g(x) = f(x − h), the shift would be to the right. Shifting the output, as in f(x) + h or f(x) − h, only moves the graph up or down, not horizontally.