# Function problem

• Dec 1st 2008, 08:45 AM
NeedHelp18
Function problem
A rectangle has a vertex on the graph of y = 9 - x^2, one in the origin, one in the positive side of the x - axis, and the fourth one on the positive side of the y - axis.

* express the area of the rectangle as a function of x
* what is the domain? ( i can prob get this when i know how to do the area one)
* wat is the area of the rectangle when x = 1.5?

• Dec 1st 2008, 12:23 PM
Soroban
Hello, NeedHelp18!

Did you make a sketch?

Quote:

A rectangle has a vertex on the graph of $\displaystyle y \:= \:9 - x^2$,
one at the origin, one on the positive x - axis, and the fourth one on the positive y - axis.

(a) Express the area of the rectangle as a function of $\displaystyle x.$

Code:

              |               *9           *  |  *       *      + - - -*     *        |::::::| *     *        |::::::|y *               |::::::|   -*----------+------+---*-               |  x      3
The area of the rectangle is: .$\displaystyle A \:=\:xy\text{, where }y \:=\:9-x^2$

Therefore: .$\displaystyle A(x) \;=\;x(9-x^2)$

Quote:

(b) What is the domain?
The domain is: .$\displaystyle 0 \,\leq\, x \,\leq\,3$

Quote:

(c) What is the area of the rectangle when $\displaystyle x = 1.5$?
$\displaystyle A(1.5) \;=\;1.5(9 - 1.5^2) \;=\;10.125$