The problem is, "to 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) $x=t;\quad y=2t+1$
(b) $x=\cos\theta;\quad y=2\cos\theta +1$
(c) $x=e^{-t};\quad y=2e^{-t}+1$
(d) $x=e^t; \quad y=2e^t+1$
The only one I am having difficulty with is (b). The graph provided in the answer key is:
Why are the arrows pointing in both directions? Is there no orientation? Also, they describe the curve as not being smooth. Why is this?
EDIT:
I have another question; the criteria given in the problem above is the same for this problem.
The parametric equations are, (a) $x=\cos\theta$, $y=2\sin^2\theta$
(b) $x=\cos(-\theta)$, $y=2\sin^2(-\theta)$
where $0<\theta<\pi$.
With the information, $-1<\cos\theta<1 \implies -1
In the answer key, however, they have $-1\le x\le1$ How did they get the "equal to" component in there?