Final answer:
True-breeding is the term used to describe an organism that consistently produces offspring with the same trait through self-pollination.
Step-by-step explanation:
The term used to describe an organism that produces only purple flowered offspring through self-pollination is true-breeding. True-breeding organisms are genetically homozygous for a particular trait and consistently pass on that trait to their offspring. In this case, the purple-flowered plant is considered true-breeding because it consistently produces purple-flowered offspring generation after generation.