Final answer:
The equation of the given exponential function is f(x) = (3/4)·(1/2)^{-x} - 4. Its domain is all real numbers, and its range is y > -4, considering the asymptote y = -4.
Step-by-step explanation:
Understanding Exponential Functions
To determine the equation of an exponential function that has been vertically compressed and reflected in the y-axis, we need to understand its transformations. Initially, the base function is f(x) = (1/2)^x. Applying a vertical compression by a factor of 3/4 changes this to f(x) = (3/4)·(1/2)^x. Since the function is reflected in the y-axis, we replace x with -x, which gives us f(x) = (3/4)·(1/2)^{-x}. Now, considering the function has an asymptote at y = -4, and its intercept is at (0, -13/4), suggests a vertical shift of -4. Thus, the function's equation is:
f(x) = (3/4)·(1/2)^{-x} - 4.
The domain of the exponential function is all real numbers, because there is no value of x for which the function is undefined. The range, however, is affected by the vertical asymptote and the transformations applied to the function. Since the asymptote is at y = -4 and the function approaches this value without ever reaching it, the range is y > -4.