y + 2 = f(x + 4)

Question

The graph of y = f(x) = bx, where b > 1, is translated such that the equation of the new graph is expressed as y + 2 = f(x + 4). The domain of the new function is

Answer 1

The initial domain of the function is all real numbers, since y = bx is just a straight line through the origin. Translating the function up 2 and left 4 will not change this: all straight diagonal lines have a domain of all real numbers.