Answer: a. To shift the graph downwards 5 units, we subtract 5 from the function, to shift it left 3 units, we add 3 to the input (the x-value), to stretch the graph vertically by a factor of 4, we multiply the function by 4, and to reflect it about the x-axis, we multiply the entire function by -1. Thus, the new function is:
g(x) = -4(1/2)^(x+3) - 5
b. To find the y-intercept, we set x=0 in the equation and solve for y:
g(0) = -4(1/2)^(0+3) - 5 = -9
Thus, the y-intercept is (0, -9).
c. The domain of the function g(x) is all real numbers, since there are no restrictions on the input x.
d. The range of the function g(x) is (-∞, -5], since the function is shifted downwards 5 units and stretched vertically by a factor of 4, which means that the maximum value of the function is -5, and it can take any value less than or equal to -5. The reflection about the x-axis does not change the range.
Explanation: