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已知定义在$\mathbb {R}$上的函数$f\left ( x \right ) $满足：①$\forall x,y \in \mathbb {R},\dfrac{f\left ( x \right )-f\left ( y \right ) }{x-y} \geqslant 0$ ；②$f\left ( x+1 \right ) =f\left ( x \right ) +1$；函数$g\left ( x \right ) =\left\{\begin{matrix}
f\left ( x \right ) ,\left | x \right | < 8 \\
f\left ( x - a \right ) ,\left | x \right | \geqslant 8
\end{matrix}\right. $，若存在实数$x_{0} $，使得$g\left ( x_{0} + 4 \right ) =g\left ( x_{0} \right ) + 1$，则$a$的取值范围为？ |
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