Which equation represents translating f(x) to the right by 5 units and upward by 2 units?

Which equation represents translating f(x) to the right by 5 units and upward by 2 units?

• A. g(x) = f(x - 5) + 2
• B. g(x) = f(x + 5) + 2
• C. g(x) = f(x - 5) - 2
• D. g(x) = f(x + 5) - 2

Answer: (A)

Shifting a graph horizontally by 5 to the right means you replace x with x minus 5 inside the function. Shifting vertically upward by 2 means you add 2 outside the function. Put together, moving right 5 and up 2 gives g(x) = f(x − 5) + 2. If you used x + 5 inside, that would move the graph left by 5. If you used −2 outside, that would move it down by 2. Mixing the signs the other way would produce left shifts or downward shifts, not the requested right and up.

Shifting a graph horizontally by 5 to the right means you replace x with x minus 5 inside the function. Shifting vertically upward by 2 means you add 2 outside the function. Put together, moving right 5 and up 2 gives g(x) = f(x − 5) + 2.

If you used x + 5 inside, that would move the graph left by 5. If you used −2 outside, that would move it down by 2. Mixing the signs the other way would produce left shifts or downward shifts, not the requested right and up.