Question

As a rocket moves farther and farther upward from the launch pad, what happens to the strength of Earth's gravitational field around the rocket?

a. It gets weaker.
b. It grows stronger.
c. It remains constant.

Answer 1

from my understanding of this, the closer to the core of the earth you are the stronger the gravity is, so it probably gets weaker. 

Answer 2

The forces of gravity between two objects are inversely proportional
to the square of the distance between them.

So the gravitational forces are stronger at closer distance, and weaker
at greater distance.

This is a big part of the reason why we are attracted more strongly to
the Earth than we are to Jupiter.