Question

The function f(x)=log₃ x-2 is translated to get g(x)=log₃ x+4. What is the effect on f(x) ?

Answer 1

The effect on the function f(x)=log₃(x-2) when translated to g(x)=log₃(x+4) is a vertical translation of the logarithmic function upwards by 6 units.

Step-by-step explanation:

The student has asked about the effect on the function f(x)=log₃(x-2) when it is translated to g(x)=log₃(x+4). This represents a vertical translation of the logarithmic function. To understand the effect, we should recall that translating a function f(x) by adding a number to the function values (i.e., f(x) + d) results in a vertical translation. In this case, the function g(x) is f(x) translated 6 units up because the +4 in g(x) is added directly to the function and compared to -2 in f(x) (4 - (-2) = 6).