Final answer:
To make a graph narrower, you can insert a coefficient greater than 1 before the variable, which in this case is inserting 3 as the coefficient (option c). Other options like adding or subtracting a number would merely shift the graph left or right.
Step-by-step explanation:
To make a graph narrower, we typically manipulate the function that is being graphed. This question seems to relate to functions and their graphs, likely in the context of algebra or precalculus.
Inserting a coefficient that is greater than 1 will compress the graph horizontally, making it narrower. In this case, inserting 3 as the coefficient (option c) of the variable will make the graph narrower.
The greater the coefficient, the more the graph is horizontally compressed. On the other hand, inserting 1/2 as the coefficient (option d) will actually make the graph wider, because it's a fraction smaller than 1 and it causes a horizontal stretch.
As a comparison, subtracting 1/2 from the end (option a) or adding 3 to the end (option b) would not make the graph narrower. These changes would shift the graph left or right, respectively.
Option C.