Answer
The sketch of $c(t)=(t^2-4t,9-t^2)$ for $-4\leq t\leq 10$.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/8c176bfc-14cf-4189-9d6c-fe03344dc0aa/result_image/1596488256.gif?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021320Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1130d65f4443bd5d08dafac125470be08424d2cc5bbca123a4d064fd05fe06b0)
Work Step by Step
Notice that $x(t)=t^2-4t$ is neither odd nor even function but that $y(t)=9-t^2$ is an even function (Figure A).
The graph $x(t)=t^2-4t$ shows that
$x(t)<0$ for $00$ for $t<0$ or $t>4$.
For the interval $-4\leq t\leq 10$, the curve starts at $c(-4)=(32,-7)$, moves to the left of $y$-axis until it reaches $y$-axis at $t=0$, $c(0)=(0,9)$. Then it moves to the right of $y$-axis until it reaches $t=4$, $c(4)=(0,-7)$, and continues moving away from the $y$-axis until $t=10$ at $c(10)=(60,-91)$ (Figure B).
![](https://gradesaver.s3.amazonaws.com/uploads/solution/8c176bfc-14cf-4189-9d6c-fe03344dc0aa/steps_image/small_1596488256.gif?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021320Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=ceac5ac7f06a53928a8e81a748f1851f79380645d8f97ee746666e515ea897dc)