x f ( x ) 0 5 1 2 3 The table above gives the values of the function f

Question

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 ?

Accepted Answer

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&rsquo;t yield the values in the table.

x	f(x)
0	5
1	$five halves$
2	$five fourths$
3	$five eighths$

Question x-f-x-