A nonconducting sheet with a large surface area and a thickness d...

Consider a Gaussian pillbox symmetric about the central plane of the sheet, with cross-sectional area $A$ and extending to a distance $x$ on both sides.

For a point inside the sheet ($0 < x < \dfrac{d}{2}$):
The charge enclosed by the Gaussian surface is $q_{\text{enclosed}} = \rho (2xA)$.
Using Gauss's law, $\oint \vec{E} \cdot d\vec{A} = \dfrac{q_{\text{enclosed}}}{\varepsilon_0}$
$E(2A) = \dfrac{\rho (2xA)}{\varepsilon_0}$
$E = \dfrac{\rho x}{\varepsilon_0}$
Thus, the electric field increases linearly with $x$ for $0 < x < \dfrac{d}{2}$.

For a point outside the sheet ($x \ge \dfrac{d}{2}$):
The total charge enclosed by the Gaussian surface is $q_{\text{enclosed}} = \rho (dA)$.
Using Gauss's law, $E(2A) = \dfrac{\rho (dA)}{\varepsilon_0}$
$E = \dfrac{\rho d}{2\varepsilon_0}$
Thus, the electric field becomes constant for $x \ge \dfrac{d}{2}$.

Therefore, the graph of $E$ against $x$ is linearly increasing for $0 < x < \dfrac{d}{2}$ and constant for $\dfrac{d}{2} \le x < d$.