Which transformation represents translating the graph of f(x) to the right by h units?

Which transformation represents translating the graph of f(x) to the right 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: (C)

Translating a graph horizontally by h units is done by replacing x with x minus h in the function. This makes every point shift to the right by h, because the value at a new x comes from the original value at x − h. So the transformed function is g(x) = f(x − h), which moves the graph to the right by h. If you used f(x + h), the shift would be to the left; if you keep the same x but subtract h from the output, you move vertically down by h, and adding h would move it vertically up.

Translating a graph horizontally by h units is done by replacing x with x minus h in the function. This makes every point shift to the right by h, because the value at a new x comes from the original value at x − h. So the transformed function is g(x) = f(x − h), which moves the graph to the right by h. If you used f(x + h), the shift would be to the left; if you keep the same x but subtract h from the output, you move vertically down by h, and adding h would move it vertically up.