Question:
Let $f(x)=\left(\frac37\right)^x$ be a function that is defined on the domain $[0,\infty)$. Find the range of the function.

Answer:
Since $\frac37$ is less than 1, the function will always decrease as $x$ increases when $x\ge0$. 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 $x\ge0$ is $\boxed{(0,1]}$