Final answer:
The restricted domain and range in the context of a marshmallow shooter involve the horizontal distance the marshmallow can travel before hitting the ground and the heights it can achieve in its trajectory, respectively.
Step-by-step explanation:
When a marshmallow shooter is shot from a height of 4 feet with an initial velocity of 12 ft/sec, we are dealing with a type of projectile motion. The restricted domain refers to the horizontal distance the marshmallow can travel before hitting the ground, which will be determined by the time it takes to fall 4 feet. Since the marshmallow cannot travel backwards or continue after it hits the ground, the restricted domain is from 0 to the point where the marshmallow lands.
The restricted range refers to the heights that the marshmallow can reach during its trajectory. As it is shot from 4 feet, the maximum height will be slightly more than 4 feet if the marshmallow is shot upwards at an angle, and it cannot go below ground level, so the restricted range is from 0 feet (ground level) to slightly above 4 feet (the maximum height attained).