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Magazine Problem 1
For the following exercises, sketch the curves below by eliminating the parameter t. Give the orientation of the curve. $$ x=t^{2}+2 t, \quad y=t+1 $$
Problem 2
For the following exercises, sketch the curves below by eliminating the parameter t. Give the orientation of the curve. $$ x=\cos (t), y=\sin (t),(0,2 \pi] $$
Problem 3
For the following exercises, sketch the curves below by eliminating the parameter t. Give the orientation of the curve. $$ x=2 t+4, y=t-1 $$
Problem 4
For the following exercises, sketch the curves below by eliminating the parameter t. Give the orientation of the curve. $$ x=3-t, y=2 t-3,1.5 \leq t \leq 3 $$
Problem 5
For the following exercises, eliminate the parameter and sketch the graphs. $$x=2 t^{2}, \quad y=t^{4}+1$$
Problem 6
For the following exercises, use technology (CAS or calculator) to sketch the parametric equations. $$ [\mathrm{T}] x=t^{2}+t, \quad y=t^{2}-1 $$
Problem 7
For the following exercises, use technology (CAS or calculator) to sketch the parametric equations. $$ \text { [T] } x=e^{-t}, \quad y=e^{2 t}-1 $$
Problem 8
For the following exercises, use technology (CAS or calculator) to sketch the parametric equations. $$ [\mathbf{T}] x=3 \cos t, \quad y=4 \sin t $$
Problem 9
For the following exercises, use technology (CAS or calculator) to sketch the parametric equations. $$ [\mathbf{T}] x=\sec t, \quad y=\cos t $$
Problem 10
For the following exercises, sketch the parametric equations by eliminating the parameter. Indicate any asymptotes of the graph. $$ x=e^{t}, \quad y=e^{2 t}+1 $$
