Which expression represents translating the graph of f(x) upward by k units?

Which expression represents translating the graph of f(x) upward by k units?

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

Answer: (B)

Shifting a graph up by a fixed number of units means every y-value increases by k. To do that with the function, you add k to the output: g(x) = f(x) + k. This raises the entire graph by k units without changing its shape. If you subtract k, it would move downward; multiplying by k changes the height scaling; and replacing x with x + k would shift the graph left. So the expression that moves the graph upward is g(x) = f(x) + k.

Shifting a graph up by a fixed number of units means every y-value increases by k. To do that with the function, you add k to the output: g(x) = f(x) + k. This raises the entire graph by k units without changing its shape. If you subtract k, it would move downward; multiplying by k changes the height scaling; and replacing x with x + k would shift the graph left. So the expression that moves the graph upward is g(x) = f(x) + k.