Textbook Problem

Comparing Plane Curves In Exercises 35-38, determine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain.

(a) $\begin{array}{l}x=t\\ y=2t+1\end{array}$

(b) $\begin{array}{l}x=\cos \theta \\ y=2\cos \theta +1\end{array}$

(c) $\begin{array}{l}x=e^{-t}\\ y=2e^{-t}+1\end{array}$

(d) $\begin{array}{l}x=e^t\\ y=2e^t+1\end{array}$