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Appendix
A-9: Graphing
Example A-9.3
Graph the curve defined parametrically by the equations $x\left(t\right)\=2tplus;1$, $y\left(t\right)\={t}^{2}-1$, for $-1\le t\le 1$.
Solution
Interactive Solution
Write a list of the parametric expressions.
Context Panel: Plots≻Plot Builder≻2-D plot (parametric) Basic Options: Set $t$: $-1$ to 1 2-D Options: scaling $\to$ constrained
$\left[2tplus;1comma;{t}^{2}-1\right]$$\to$
Alternatively, launch the with the given function already installed. (The Preview and Options buttons will work, but no graph will be embedded in this worksheet.) The graph drawn with the Plot Builder nearly results in Figure A-9.3(b), which was drawn with the plot command hidden behind the cell in with the figure appears.
Defaults to 2-D parametric plot Set $-1\le t\le 1$ and press Preview or Plot See Figure A-9.3(a)
Figure A-9.3(a) Interactive Plot Builder launched on a list
Figure A-9.3(b) Graph of parametrically defined curve.
The astute reader will note that the axes are labeled with $x$ and $y$, but this is not possible with the Interactive Plot Builder. Figure A-9.3(c) shows that there is no provision for labeling axes when the Interactive Plot Builder is used to graph a parametrically defined curve.${}$
The Interactive Plot Builder for the sequence $x\left(t\right)\,y\left(t\right)$ will default to the graph of two separate curves. If the Plot Builder is launched on a sequence instead of a list, select "2-D parametric plot" to obtain the graph of the parametrically-defined curve. See Figure A-9.3(d).
Figure A-9.3(c) Relevant part of Options panel in the Interactive Plot Builder
Figure A-9.3(d) Interactive Plot Builder launched on a sequence, not list
Coded Solution
Execute the plot command shown to the right.
$\mathrm{plot}\left(\left[2tplus;1comma;{t}^{2}-1comma;tequals;-1..1\right]comma;\mathrm{labels}equals;\left[xcomma;y\right]\right)$
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