The process by which a modified stem or root of a parent plant grows offspring that remain attached is called

vegetative reproduction
binary fission
tuber reproduction
fragmentation

vegetative reproduction

The correct answer is vegetative reproduction.

The correct answer is vegetative reproduction. To arrive at this answer, first, let's understand what each of the options means:

1. Vegetative reproduction: This is a form of asexual reproduction in plants where a stem or root of a parent plant produces offspring that remain attached to the parent plant. Examples of vegetative reproduction include runners, bulbs, and rhizomes.

2. Binary fission: This is a form of reproduction commonly seen in single-celled organisms, such as bacteria and some protists. It involves the division of a single organism into two identical daughter cells.

3. Tuber reproduction: A tuber is a swollen underground stem that stores nutrients, such as in the case of potatoes. While tubers can give rise to new plants, they are not known to grow offspring that remain attached to the parent plant as described in the question.

4. Fragmentation: Fragmentation is a form of asexual reproduction in which an organism breaks into several pieces, each of which can grow into a separate individual. This process is commonly seen in some plants, such as mosses and ferns, as well as in some animals like starfish.

Considering the definitions of the given options, the best-fitting term for the process described in the question is vegetative reproduction.