Question

Which transformation takes the graph of f(x) = 4^x to the graph of g(x) = 4^x − 3?

a) The graph is translated up 3 units.
b) The graph is translated to the left 3 units.
c) The graph is translated to the right 3 units.
d) The graph is translated down 3 units.​

Answer 1

The transformation that takes the graph of f(x) = 4^x to the graph of g(x) = 4^x − 3 is a vertical translation downwards by 3 units.

To see why, note that the function g(x) is obtained by subtracting 3 from the output (or y-value) of the function f(x) for every value of x. This means that the graph of g(x) is obtained by shifting the graph of f(x) downwards by 3 units.

Therefore, the correct answer is:

d) The graph is translated down 3 units.