What is the range of f(x) = (3/4)^x – 4

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asked May 7, 2018 56.5k views

2 Answers

Denis Wang · Answer 1 · 2018-05-08T08:39:57+0000

The range of f(x) = (3/4)^x - 4 is (-∞, -4].

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].