jmc

Since $\frac{3}{7}$ is less than 1, the function will always decrease as $x$ increases when $x\ge 0$. So, the largest value in the range will occur when at the smallest value of $x$: $x=0$, giving us the upper bound of ${\left(\frac{3}{7}\right)}^0=1$. As the value of $x$ increases, the value of $y$ will gradually decrease, approaching (but never reaching) the lower bound of 0. Therefore, the range of this function when $x\ge 0$ is $\boxed{(0,1]}$