Predicting the nature of filters
If you know your filter is simple and you just want to classify it as low pass or high pass, you only need to find two frequencies at which the response differs.  As the name says, "low pass" passes low frequencies and by implication attenuates high frequencies.  A "high pass" does the opposite.  If the filter shows a higher response from the low frequency than the high, then it is low pass.  A high pass filter will show a higher response for the higher frequency.

Generally the "filter response" is it's gain as a function of frequency.  Therefore looking at its response at high and low frequencies is measuring it directly, not somehow inferring it.

There are clever ways to infer the frequency response of a filter from its response to various single events in the time domain, like a step or a blip.  Those do require some cleverness and use of Fourier's math, but that is not what you asked about.