Question

For the function f(x) = 3x, what is the translation for g(x) = f(x) 2 and the new function g(x)?

A) g(x) 3x+2
B) down 2
C) up 2
D) g(x) = 3x-2
E) g(x) = -3x - 2

Answer 1

The translation of the function f(x) = 3x by g(x) = f(x) + 2 results in a vertical shift upwards by 2 units, leading to the new function g(x) = 3x + 2.

Step-by-step explanation:

For the function f(x) = 3x, the translation for g(x) = f(x) + 2 would be a vertical shift upwards by 2 units. This is because adding a positive constant to the entire function affects the y-values directly. Therefore, the new function g(x) becomes g(x) = 3x + 2.