Question

If f(x) (in blue) is a translation of g(x) (in red), what is the translation?

f(x)=2^x+2 +1
f(x)=2^x-3 -1
f(x)=2^x-3 +1
f(x)=2^x+3 -1

Answer 1

Function f(x) has been translated 3 units to the right and 1 unit up from function g(x), which corresponds to f(x) = 2^(x-3) + 1.

Step-by-step explanation:

If we have two functions f(x) and g(x), and we are told that f(x) is a translation of g(x), this means that we have shifted g(x) horizontally, vertically, or both to get f(x). Specifically, f(x) = 2x - d + k would represent g(x) = 2x translated d units to the right and k units up. Looking at the given options for f(x), f(x) = 2x - 3 + 1 implies that g(x) has been shifted 3 units to the right and 1 unit up.

When we compare the given function f(x) = 2^x+2 + 1 to g(x), we can identify the translation by looking at the constant term. In this case, the constant term in f(x) is +1, while in g(x) it is -1.

A positive constant on the end of the function indicates a translation in the positive y-direction, while a negative constant indicates a translation in the negative y-direction. Therefore, the translation is in the positive y-direction.

So, the correct translation would be given by the option f(x) = 2^x-3 + 1.