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Advanced Math / Nonlinear functions Difficulty: Medium

$q left parenthesis x right parenthesis equals 32 left parenthesis 2 Superscript x Baseline right parenthesis$

Which table gives three values of $x$ and their corresponding values of $q (x)$ for function $q$ ?

$x$	$negative 1$	$0$	$1$
$q (x)$	$negative 64$	$0$	$64$

$x$	$negative 1$	$0$	$1$
$q (x)$	$\frac{1}{16}$	$2$	$64$

$x$	$negative 1$	$0$	$1$
$q (x)$	$\frac{1}{16}$	$32$	$64$

$x$	$negative 1$	$0$	$1$
$q (x)$	$16$	$32$	$64$

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Explanation

Choice D is correct. Substituting $negative 1$ for $x$ in the given function yields $q (- 1) = 32 {(2)}^{- 1}$ , which is equivalent to $q (- 1) = 32 (\frac{1}{2})$ , or $q (- 1) = 16$ . Therefore, when $x = - 1$ , the corresponding value of $q (x)$ for function $q$ is $16$ . Substituting $0$ for $x$ in the given function yields $q left parenthesis 0 right parenthesis equals 32 left parenthesis 2 right parenthesis Superscript 0$ , which is equivalent to $q left parenthesis 0 right parenthesis equals 32 left parenthesis 1 right parenthesis$ , or $q left parenthesis 0 right parenthesis equals 32$ . Therefore, when $x equals 0$ , the corresponding value of $q (x)$ for function $q$ is $32$ . Substituting $1$ for $x$ in the given function yields $q left parenthesis 1 right parenthesis equals 32 left parenthesis 2 right parenthesis Superscript 1$ , which is equivalent to $q left parenthesis 1 right parenthesis equals 32 left parenthesis 2 right parenthesis$ , or $q left parenthesis 1 right parenthesis equals 64$ . Therefore, when $x equals 1$ , the corresponding value of $q (x)$ for function $q$ is $64$ . Of the choices given, only the table in choice D gives these three values of $x$ and their corresponding values of $q (x)$ for function $q$ .

Choice A is incorrect. This table gives three values of $x$ and their corresponding values of $q (x)$ for the function $q left parenthesis x right parenthesis equals 32 left parenthesis 2 x right parenthesis$ .

Choice B is incorrect. This table gives three values of $x$ and their corresponding values of $q (x)$ for the function $q left parenthesis x right parenthesis equals 2 left parenthesis 32 right parenthesis Superscript x$ .

Choice C is incorrect and may result from conceptual or calculation errors.