To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.
Let's choose some x-values and calculate the corresponding y-values:
For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4
For x = -1, y = 4(4)^(-1) = 4(1/4) = 1
For x = 0, y = 4(4)^0 = 4(1) = 4
For x = 1, y = 4(4)^1 = 4(4) = 16
For x = 2, y = 4(4)^2 = 4(16) = 64
Now we can plot these points on a coordinate plane and connect them to form the graph of the function.
The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.
The domain of the function is all real numbers since there are no restrictions on the values of x.
The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.