Set 5: Polynomial Functions (Intermediate)
Explanation
For the exponential function f, the value of f (1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?
Choose the correct answer.
f (x ) = 128(1.6)x−1
f (x ) = 80(1.6)x
f (x ) = 50(1.6)x+1
f (x ) = 204.8(1.6)x−2 - 22 - - - - - - –5x + 13 = 73
Detailed Explanation
Choice A is correct. For the form of the function in choice C, f ^xh= 128 ^1.6 hx - 1 , the value of f ^1 h can be found as 128 ^1.6 h 1 - 1 , which is equivalent to 128 ^1.6 h 0 , or 128. Therefore, k = 128, which is shown in f ^xh= 128 ^1.6 hx - 1 as the coefficient. Choice C is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
Key Steps:
The correct answer is f (x ) = 128(1.6)x−1
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