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Choice A is correct. The value of $h\left(-2\right)$ can be found by substituting $-2$ for $x$ in the equation defining $h$. Substituting $-2$ for $x$ in $h\left(x\right)=3x-7$ yields $h\left(-2\right)=3\left(-2\right)-7$, or $h\left(-2\right)=-13$. Therefore, the value of $h\left(-2\right)$ is $-13$.

Choice B is incorrect. This is the value of $h\left(-1\right)$, not $h\left(-2\right)$.

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

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