| x | f (x) |
| 0 | 5 |
| 1 |
|
| 2 |
|
| 3 |
|
The table above gives the values of the function f for some values of x. Which of the following equations could define f ?
Correct answer: D
Explanation
Choice D is correct. Each choice has a function with coefficient 5 and base 2, so the exponents must be analyzed. When the input value of x increases, the output value of f(x) decreases, so the exponent must be negative. An exponent of –x yields the values in the table: ,
,
, and
.
Choices A and B are incorrect and may result from choosing equations that yield an increasing, rather than decreasing, output value of f(x) when the input value of x increases. Choice C is incorrect and may result from choosing an equation that doesn’t yield the values in the table.
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