SAT question dba7432e (Nonlinear Functions)

Question

The table above gives the values of the function f for some values of x . Which of the following equations could define f ?

College Board · Accepted Answer

The correct answer is D. 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: 5 = 5(2^0) , 5/2 = 5(2^-1) , 5/4 = 5(2^-2) , and 5/8 = 5(2^-3) .

CookSAT · Answer

Note: Graph the table’s points and test the answer choices; choice D’s curve passes through every listed point.

$x$	$f (x)$
$0$	$5$
$1$	$\frac{5}{2}$
$2$	$\frac{5}{4}$
$3$	$\frac{5}{8}$

Explanation

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Why the other choices are wrong

SAT Question dba7432e: Nonlinear Functions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong