Hold Still....

It isn't until Jesse gets back to civilization that she really begins to learn things about the "dog that followed her home". Her Japanese friend, Mikki Kakubari, who is a college friend helps her by translating InuYasha's difficult old Japanese way of speaking to English.

During those conversations, she learns about Kagome, and InuYasha's other connection to the modern world. Clearly, he misses her...

This is before he gains his stripes and more dangerous nature.