Q1 TF. - Calculus

Question

Parametric curves: Imagine the curve traced in the xy-plane by

the coordinates (x, y) = (3z + 1, $z^2$− 4) as z varies, where the

parameter z is a function of time t.

 Plot the points (x, y) in the plane that correspond to

z = −3,−2,−1, 0, 1, 2, and 3

Step-by-Step Solution

Answer

Step 1. Given Information

$(x,y)=(3z+1,z^2-4)$

Step 2. Calculation

For $z=-3$

$(x,y)=(-8,5)$

For $z=-2$

$(x,y)=(-5,0)$

For $z=-1$

$(x,y)=(-2,-3)$

For $z=0$

$(x,y)=(1,-4)$

For $z=1$

$(x,y)=(4,-3)$

For $z=2$

$(x,y)=(7,0)$

For $z=3$

$(x,y)=(10,5)$

Step 3. Graph