For a uniformly charged solid non-conducting sphere of radius $R$ carrying a total charge $Q$:

1. Inside the sphere ($r < R$): The electric field is directly proportional to the distance from the center. Using Gauss's Law, the field is given by $E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{R^3} r$. Thus, $E \propto r$, which represents a straight line passing through the origin.
2. At the surface ($r = R$): The field reaches its maximum value, $E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{R^2}$.
3. Outside the sphere ($r \ge R$): The sphere behaves like a point charge concentrated at the center. The electric field follows the inverse square law: $E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2}$. Thus, $E \propto \frac{1}{r^2}$, which represents a hyperbola.

The correct graph must show a linear increase from the origin to $r=R$ and a hyperbolic decrease for $r > R$.