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Advanced Math / Nonlinear functions Difficulty: Easy

$h (x) = x^{2} - 3$

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

$x$	$1$	$2$	$3$
$h (x)$	$4$	$5$	$6$

$x$	$1$	$2$	$3$
$h (x)$	$negative 2$	$1$	$6$

$x$	$1$	$2$	$3$
$h (x)$	$negative 1$	$1$	$3$

$x$	$1$	$2$	$3$
$h (x)$	$negative 2$	$1$	$3$

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Explanation

Choice B is correct. It′s given that $h (x) = x^{2} - 3$ . Each table gives $1$ , $2$ , and $3$ as the three given values of $x$ . Substituting $1$ for $x$ in the equation $h (x) = x^{2} - 3$ yields $h (1) = {(1)}^{2} - 3$ , or $h (1) = - 2$ . Substituting $2$ for $x$ in the equation $h (x) = x^{2} - 3$ yields $h (2) = {(2)}^{2} - 3$ , or $h left parenthesis 2 right parenthesis equals 1$ . Finally, substituting $3$ for $x$ in the equation $h (x) = x^{2} - 3$ yields $h (3) = {(3)}^{2} - 3$ , or $h left parenthesis 3 right parenthesis equals 6$ . Therefore, $h (x)$ is $negative 2$ when $x$ is $1$ , $h (x)$ is $1$ when $x$ is $2$ , and $h (x)$ is $6$ when $x$ is $3$ . Choice B is a table with these values of $x$ and their corresponding values of $h (x)$ .

Choice A is incorrect. This is a table of values for the function $h (x) = x + 3$ , not $h (x) = x^{2} - 3$ .

Choice C is incorrect. This is a table of values for the function $h (x) = 2 x - 3$ , not $h (x) = x^{2} - 3$ .

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