Final answer:
The range of f(x) = (3/4)^x - 4 is (-∞, -4].
Step-by-step explanation:
The range of the function f(x) = (3/4)^x - 4 can be determined by finding the minimum and maximum values that the function can reach.
- First, let's determine the minimum value of f(x). The base of the exponent, 3/4, is less than 1, which means that as x approaches positive or negative infinity, the function approaches negative infinity. Therefore, the minimum value of f(x) is negative infinity.
- Next, let's determine the maximum value of f(x). Since the base is less than 1, as x approaches positive or negative infinity, the function approaches 0. However, f(x) can never actually reach 0 because of the constant -4 subtracted from it. Therefore, the maximum value of f(x) is -4.
Putting it all together, the range of f(x) is (-∞, -4].