Explanation

(c) $Z = \sqrt{R^{2} + \left( 2\pi fL - \frac{1}{2\pi fC} \right)^{2}}$
From above equation at $f = 0,\ z = \infty$
When $f = \frac{1}{2\pi\sqrt{LC}}$ (resonant frequency) $\Rightarrow Z = R$
For $f > \frac{1}{2\pi\sqrt{LC}} \Rightarrow Z$ starts increasing
$i.e.,$ for frequency $0 - f_{r},\ Z$ decreases and for $f_{r}$ to $\infty,\ Z$ increases
This is justified by graph $c$