Example Question - horizontal translation

Logarithmic Function Transformations

The given logarithmic function f(x) = ln x is transformed to g(x) = ln(x - 2) + 5. Comparing the function g(x) with f(x): 1. The "+ 5" at the end of g(x) indicates a vertical translation upward by 5 units. 2. The "(x - 2)" inside the logarithm in g(x) suggests a horizontal translation to the right by 2 units since the effect of subtracting inside the function argument is to shift the graph to the right. Given the options provided: A. f(x) is translated up 5 units. (This is correct for the vertical translation.) B. f(x) is translated down 2 units. (This is incorrect; the function is not translated downward.) C. f(x) is translated left 2 units. (This is incorrect; the function is actually translated right.) D. f(x) is translated right 5 units. (This is incorrect; the translation is 2 units to the right, not 5.) Therefore, the correct answer is A. f(x) is translated up 5 units.