An exponential function with a base of 1/2 has been vertically compressed by a factor of 3/4 and reflected in the x-axis. It's asymptote is the line y = - 4. What is the equation of the function?

We are asked in this problem to determine the expression of an exponential function given the data above. The standard form of an exponential function is expressed as y = a^x + b was a is the base constant and b is another constant. In this case, a is given to be equal to 1/2. since the graph is said to be shrunk down to 3/4 then the initial expression would have to be y = 3/4 * (1/2) ^x + b. b is determined through the given asymptote in the problem. An asymptote is an axis or the line in which the graph approaches but never touches. b is equal to - 4. In this case, the overall expression is y = 3/4 * (1/2) ^x - 4.