what was the function of the Roman cavalry?

[L C Cinna]

for the 120 men legionary cavalry:

Scouting and VERY important communication on the battlefield.


For other cavalry forces:

Scouting, chasing routing enemies, screening the infantry before battle, protecting the flanks, harassing and attacking the enemy from the sides and rear.

They could and would attack and charge but only if the situation allowed. A good thing to read is Joephus Judaean war 3rd book:

These Jews, therefore, out of their anger, marched faster than ordinary, and, as if they had come but a little way, approached very near the city, and were come even to it; but Antonius, who was not unapprized of the attack they were going to make upon the city, drew out his horsemen beforehand, and being neither daunted at the multitude, nor at the courage of the enemy, received their first attacks with great bravery; and when they crowded to the very walls, he beat them off. Now the Jews were unskillful in war, but were to fight with those who were skillful therein; they were footmen to fight with horsemen; they were in disorder, to fight those that were united together; they were poorly armed, to fight those that were completely so; they were to fight more by their rage than by sober counsel, and were exposed to soldiers that were exactly obedient; and did every thing they were bidden upon the least intimation. So they were easily beaten; for as soon as ever their first ranks were once in disorder, they were put to flight by the enemy's cavalry, and those of them that came behind such as crowded to the wall fell upon their own party's weapons, and became one another's enemies; and this so long till they were all forced to give way to the attacks of the horsemen, and were dispersed all the plain over, which plain was wide, and all fit for the horsemen; which circumstance was very commodious for the Romans, and occasioned the slaughter of the greatest number of the Jews; for such as ran away, they could overrun them, and make them turn back; and when they had brought them back after their flight, and driven them together, they ran them through, and slew a vast number of them, insomuch that others encompassed others of them, and drove them before them whithersoever they turned themselves, and slew them easily with their arrows; and the great number there were of the Jews seemed a solitude to themselves, by reason of the distress they were in, while the Romans had such good success with their small number, that they seemed to themselves to be the greater multitude. And as the former strove zealously under their misfortunes, out of the shame of a sudden flight, and hopes of the change in their success, so did the latter feel no weariness by reason of their good fortune; insomuch that the fight lasted till the evening, till ten thousand men of the Jews' side lay dead, with two of their generals, John and Silas, and the greater part of the remainder were wounded, with Niger, their remaining general, who fled away together to a small city of Idumea, called Sallis. Some few also of the Romans were wounded in this battle.

[485] As Titus was saying this, an extraordinary fury fell upon the men; and as Trajan was already come before the fight began, with four hundred horsemen, they were uneasy at it, because the reputation of the victory would be diminished by being common to so many. Vespasian had also sent both Antonius and Silo, with two thousand archers, and had given it them in charge to seize upon the mountain that was over against the city, and repel those that were upon the wall; which archers did as they were commanded, and prevented those that attempted to assist them that way; And now Titus made his own horse march first against the enemy, as did the others with a great noise after him, and extended themselves upon the plain as wide as the enemy which confronted them; by which means they appeared much more numerous than they really were. Now the Jews, although they were surprised at their onset, and at their good order, made resistance against their attacks for a little while; but when they were pricked with their long poles, and overborne by the violent noise of the horsemen, they came to be trampled under their feet; many also of them were slain on every side, which made them disperse themselves, and run to the city, as fast as every one of them were able. So Titus pressed upon the hindmost, and slew them; and of the rest, some he fell upon as they stood on heaps, and some he prevented, and met them in the mouth, and run them through; many also he leaped upon as they fell one upon another, and trod them down, and cut off all the retreat they had to the wall, and turned them back into the plain, till at last they forced a passage by their multitude, and got away, and ran into the city.