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Which of the following functions has(have) a −3 minimum value at? = −6 3^x −3 I. f x = −3 6^x II. g x
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
= x+ 1 2 Choice D is correct. A function of the form f^xh a^bh c, where a 0 and b 1, is a decreasing function. Both of the given functions are of this form; therefore, both are decreasing functions. If a function f is decreasing, as the value of x increases, the corresponding value of f^xh decreases; therefore, the function doesn’t have a minimum value. Thus, neither of the given functions has a minimum value. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.
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