If I had to go blind, plotting the frequency spectrum should tell you if you have a task - but of course we usually also have the design to match the time series. So you can check which frequency is the task in the design and this should more or less match the fMRI time series (I'm assuming you have two time series and don't know which one is rest and which one is task).

Is there a difference between rest and task fMRI signals.By this I mean that, given a time series of activations, how can one verify if it can correspond to a voxel time-series from a task-based fMRI study?