Question x-f-x-
| 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 ?
x f ( x ) 0 5 1 2 3 The table above gives the values
Hard-difficulty · SAT Math · Nonlinear Functions — Function composition and evaluation. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer 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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