When $x$ grams of NaCl are added to water in a beaker and the temperature is increased from $1^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$, the molarity of the solution changes due to the volumetric changes of water.

Temperature from $1^{\circ} \mathrm{C}$ to $4^{\circ} \mathrm{C}$:

Water is densest at $4^{\circ} \mathrm{C}$.

As the temperature increases from $1^{\circ} \mathrm{C}$ to $4^{\circ} \mathrm{C}$, the water volume decreases due to increased density.

This decrease in volume results in an increase in molarity because molarity is inversely proportional to the solution's volume.

Temperature from $4^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$:

Beyond $4^{\circ} \mathrm{C}$, water expands with an increase in temperature.

Therefore, as temperature rises to $25^{\circ} \mathrm{C}$, the volume of the water increases.

The dilution leads to a decrease in molarity, since molarity is inversely proportional to volume.

Thus, the molarity first increases as temperature rises to $4^{\circ} \mathrm{C}$, but then decreases as it continues to $25^{\circ} \mathrm{C}$. The graphical representation of this relationship would exhibit an initial increase in molarity, followed by a decrease, correlating with changes in the volume of water due to temperature variations.