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) - 2g(x) = f(x) + 2g(x) = f(x + 2)
Accepted Solution
A:
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