sat-dog

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

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

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

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