Free SAT Practice Question

For all integers $x>0$, let $f\left(x\right)$ be defined as $f\left(x\right)=\dfrac{f\left(x - 1\right)}{{\left(-1\right)}^x}$. If $f\left(1\right)=1$, which of the following statement is correct for the values of $f\left(x\right)$? (without calculator)