# parametric equation question

• Mar 25th 2009, 01:01 PM
oceanmd
parametric equation question
Please explain how to do the following problem.
Graph the following parametric equation. Identify the domain and range. Eliminate the parameter.
x = sq.root of t
y = 2 – sq.root of t

Thank you very much
I did a table for
t = 0, 1, 4, 9
x = 0, 1, 2, 3
y = 2, 1, 0, -1

Positioned the dots (x,y), it's a line Domain (-infinity, +infinity), Range (-infinity, +infinity). When I eliminated the parameter, the equation is y=2-x
Does it make any sense? Thank you again.
• Mar 25th 2009, 01:16 PM
running-gag
Hi

Your work is OK except for the domain and range

$\displaystyle x=\sqrt{t}$ and $\displaystyle y=2-\sqrt{t}$ are defined only for $\displaystyle t \geq 0$ which means $\displaystyle x \geq 0$ and $\displaystyle y \leq 2$

Therefore the graph is not a complete line but a "semi-line" starting from the point (0,2)
• Mar 25th 2009, 01:17 PM
Pinkk
The domain is not $\displaystyle (-\infty,\infty)$, and neither is the range.

$\displaystyle x=\sqrt{t}$ is only defined when $\displaystyle t\ge 0$, which means $\displaystyle x\ge 0$, so your domain is $\displaystyle [0,\infty)$

Likewise, $\displaystyle y=2-\sqrt{t}$ is only defined when $\displaystyle t\ge 0$, which means $\displaystyle y\le 2$, so the range of the function is $\displaystyle (-\infty,2]$.

The equation IS $\displaystyle y=2-x$, but we must restrict the domain to $\displaystyle [0,\infty)$ because of the parameters we were initially given.
• Mar 25th 2009, 03:17 PM
oceanmd
Thank you
running-gag and Pinkk,

Thank you very much.