Final answer:
The polymer with both 1-4 and 1-6 glycosidic bonds between alpha glucose molecules is amylopectin or glycogen, both of which are branched polysaccharides differing in their degree of branching.
Step-by-step explanation:
The polymer that is joined by 1-4 and 1-6 glycosidic bonds between alpha glucose molecules is amylopectin or glycogen.
Amylopectin is a branched-chain polysaccharide composed of glucose units linked mainly by α-1,4-glycosidic bonds, with the occasional α-1,6-glycosidic bond providing the branching. This branching occurs about every 25-30 glucose units, altering the helical structure to create a reddish brown color when iodine is present, in contrast to the deep blue-violet color of amylose.
Glycogen, which is not explicitly depicted in the reference figures, is similar to amylopectin but with a higher degree of branching. Therefore, the correct answer to the student's question is either amylopectin or glycogen, depending on the context given by the educator or source material.