Down towards the soil line on the trunk of the tree, look for a change in trunk texture or size. If the tree isn't too big, look for what looks like a 'V' or slash where the root and the trunk came together. If you can, send a photo of the tree trunk from ground level up and we will look too.
Your tree could be seed grown but if it was produced commercially, it is grafted. The growers can get a jump start on tree size by grafting. Very few commercially grown trees are not grafted.
If its a variety, a horticulturist may be able to give you a name.
Rooting a cutting is still an option. It sould be able to handle your Texas summers.
Daisy