Chapter 10.1, Problem 28E

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) $x=\sin 2t,y=\sin \left(t+\sin 2t\right)$

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

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

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