Answer:
the domain is "the set of all real numbers."
the range of the given function is (5, infinity)
Step-by-step explanation:
This is an exponential function. For the sake of clarity you must enclose "x - 2" inside parentheses: f(x) = 2(3)^(x-2). This function is defined for all real x-values, so the domain is "the set of all real numbers."
Focusing on (3)^x: This has the same shape as the basic exponential y = e^x; the graph starts in Quadrant II and increases with x, more and more rapidly as you pass x = 0. The functions y = e^x and that of y = 3^x are always positive. Likewise in the case of f(x) = 2(3)^(x-2): the function is always positive. If we look at f(x) = 2(3)^(x-2) alone, we conclude that the domain is (0, infinity). But that " + 5 " in y=2(3)^(x-2) + 5 translates the entire graph of f(x) = 2(3)^(x-2) upward by 5 units.
Thus, the range of the given function is (5, infinity).
