Problems

01

Convert parametric curve to function graph

Write the following curves as the graphs of a function $y=f(x)$. (Find $f(x)$ for each case.)

(a) $x=t+3$, $y=4t$ and $0<t<1$

(b) $x=\cos t$, $y={\sin }^{2}t$ and $0<t<2\pi$

Sketch each curve.

02

Convert parametric curve to function graph

Write the following curves as the graphs of a function $y=f(x)$. (Find $f(x)$ for each case.)

(a) $x=t$, $y=t$ and $-\infty <t<\infty$

(b) $x=e^t$, $y=e^t$ and $-\infty <t<\infty$

Sketch each curve.

03

Convert function graph to parametric curve

Find parametric curves $c(t)=(x(t),y(t))$ whose images are the following graphs:

(a) $y=3x-4$ and $c(0)=(\mathrm{2,2})$

(b) $y=3x-4$ and $c(3)=(\mathrm{2,2})$