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Which of the following is not a key feature of the function f(x) = (1/4)^x?

a. The domain includes all real numbers.
b. The range is y > 0.
c. The y-intercept is at (0, 1).
d. The function grows exponentially.

1 Answer

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Final answer:

The statement that the function f(x) = (1/4)^x grows exponentially is incorrect; the function decays exponentially since the base is less than 1. The domain includes all real numbers, the range is y > 0, and the y-intercept is at (0, 1).

Step-by-step explanation:

The correct answer to the question of which of the following is not a key feature of the function f(x) = (1/4)x is d. The function grows exponentially. Given the base of the exponential function is less than 1, the function actually decays, or decreases, exponentially as x increases. The remaining statements are true for the function: a) The domain does include all real numbers as there are no restrictions on the values x can take. b) The range is y > 0 because exponential functions with positive bases never reach zero and hence, never produce negative values or zero. c) The y-intercept is indeed at (0, 1), because any base raised to the power of 0 is 1.

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