Question

Describe how to transform the graph of g(x) = ln(x) into the graph of f(x) = ln(x - 4) + 3.

a. Translate 4 units to the left and 3 units up
b. Translate 4 units to the right and 3 units down
c. Translate 4 units to the right and 3 units up
d. Translate 3 units to the left and 4 units down

Answer 1

To transform the graph of g(x) = ln(x) to f(x) = ln(x - 4) + 3, translate the graph 4 units to the right and 3 units up.

Step-by-step explanation:

To transform the graph of g(x) = ln(x) into the graph of f(x) = ln(x - 4) + 3, we must perform two translations on the graph of g(x). Firstly, the term (x - 4) inside the logarithm indicates a horizontal shift to the right by 4 units since we must add 4 to x to return to the original function g(x). Secondly, the + 3 outside the logarithm indicates a vertical shift upwards by 3 units. So, the correct transformation is to translate the graph 4 units to the right and 3 units up, which corresponds to option c.