Chapter 1.7, Problem 23E

To determine

To find: The sketch for the parametric curve.

Explanation of Solution

Given:

The given graph is shown in Figure 1

  

Figure 1

Calculation:

From the graph the value of $x$ and $y$ for the different values of $t$ is,

For $t=0$

  $\begin{array}{l}x=-1\\ y=0\end{array}$

For $t=-1$

  $\begin{array}{l}x=0\\ y=-1\end{array}$

For $t=1$

  $\begin{array}{l}x=0\\ y=1\end{array}$

The parametric curve passes through the points $\left(-1,0\right),\left(0,-1\right)$ and $\left(0,1\right)$ . The direction of the curve is from $\left(0,-1\right)$ to $\left(0,1\right)$ and it passes through the point $\left(-1,0\right)$ .

The sketch for the parametric curve is shown in Figure 2