f x = 272 2 x The function f is defined by the given equation. If

Choice A is correct. It's given that $f\left(x\right)=272(2{)}^x$ and $h\left(x\right)=f(x-4)$. Substituting $x-4$ for $x$ in $f\left(x\right)=272(2{)}^x$ yields $f\left(x-4\right)=272{\left(2\right)}^{x-4}$. Substituting $h\left(x\right)$ for $f\left(x-4\right)$ in this equation yields $h\left(x\right)=272{\left(2\right)}^{x-4}$. Using the properties of exponents, the function $h\left(x\right)=272(2{)}^{x-4}$ can be rewritten as $h\left(x\right)=\frac{272{\left(2\right)}^x}{2^4}$, which is equivalent to $h\left(x\right)=\frac{272{\left(2\right)}^x}{16}$, or $h\left(x\right)=17(2{)}^x$. Therefore, of the given choices, an equation that defines function $h$ is $h\left(x\right)=17(2{)}^x$.

Choice B is incorrect. This equation defines function $h$ if $h\left(x\right)=f(x-2)$, not $h\left(x\right)=f(x-4)$.

Choice C is incorrect. This equation defines function $h$ if $h\left(x\right)=f\left(4x\right)$, not $h\left(x\right)=f(x-4)$.

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