Match the parametric equations with the graphs labeled I-VI. Give reasons for your choices. (Do not use a graphing device.)

(a) $ x = t^4 - t + 1 $, $ \; y = t^2 $

(b) $ x = t^2 - 2t $, $ \; y = \sqrt{t} $

(c) $ x = \sin 2t $, $ \; y = \sin(t + \sin 2t) $

(d) $ x = \cos 5t $, $ \; y = \sin 2t $

(e) $ x = t + \sin 4t $, $ y = t^2 + \cos 3t $

(f) $ x = \dfrac{\sin 2t}{4 + t^2} $, $ \; y = \dfrac{\cos 2t}{4 + t^2} $