Match the parametric equations with the graphs labeled

I-VI. Give reasons for your choices. (Do not use a graphing device.)

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

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

(b) $x=t^{2}-2 t, \quad y=\sin (t+\sin 2 t)$

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

(d) $x=\cos 5 t, \quad y=t^{2}+\cos 3 t$

(e) $x=\frac{\sin 2 t}{4+t^{2}}, \quad y=\frac{\cos 2 t}{4+t^{2}}$