1. ## 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.

2. Hi

Your work is OK except for the domain and range

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

Therefore the graph is not a complete line but a "semi-line" starting from the point (0,2)

3. The domain is not $(-\infty,\infty)$, and neither is the range.

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

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

The equation IS $y=2-x$, but we must restrict the domain to $[0,\infty)$ because of the parameters we were initially given.

4. ## Thank you

running-gag and Pinkk,

Thank you very much.