Question

Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.

Which of the rules given below shows the transformation of f?

g(x) = f(x - 2)

g(x) = f(x) - 2

g(x) = f(x) + 2

g(x) = f(x + 2)

Answer 1

Plato fellows, I tried that answer ITS WRONG

Explanation:

but literally just because of the placement of parenthesis, here's the correct answer. the correct answer in fact is,

D. g(x) = f(x + 2)

Answer 2

The first thing we are going to do in this case is to take into account the following definition.
Translations are transformations that change the position of the graph of a function.
The general shape of the graph of a function is moved up, down, to the right or to the left.
The translations are considered rigid transformations. Now we will see how these are performed.
Vertical translations:
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
To graph y = f (x) -k, move the graph of k units down.
Using the definition we conclude that:
g (x) = f (x) - 2
Answer:
g (x) = f (x) - 2