y = 6(2)^(x-4)-1 is an exponential function with a base of 2 and an exponent of x-4. The coefficient of the base, 6, is called the leading coefficient. The constant term, -1, is the y-intercept, the point where the graph of the function crosses the y-axis. The function is also a shifted version of the basic exponential function y= a*b^x, where a is the leading coefficient and b is the base of the function.
Since the base of the function is 2, the graph of the function will increase or decrease at an increasing rate. The leading coefficient of 6 will affect the steepness of the graph, making it steeper than the basic exponential function y=2^x. The horizontal shift of the graph is 4 units to the left, as the exponent has x-4 instead of x.
In terms of symmetry, the graph of this function has no symmetry.
The function has no rotational symmetry because it is not repeated after any rotation around the origin.