Question

The area of this rectangle is given by the quadratic function

A = 50W - W2.

What is the reasonable domain for this function?
A) 0 < x < 50
B) 0 < x < 100
C) 0 < x < ∞
D) −∞ < x < ∞

Answer 1

Answer:A

Step-by-step explanation:I did and I got it correct

Answer 2

The function uses W as the variable but the options show only x's as the variable, so I'm asumming W in the answer

Answer:

0 < W < 50

Correct option: A

Explanation:

Domain of functions

Some functions have restricted values of the independent variable x. It can be due to mathematical restrictions, like dividing by 0 or taking the square root of a negative number, of it can be due to practical conditions of the situation being modeled.

In this case, the area of a rectangle is given by the quadratic function.

`A=50W - W^2`

Since the area of a rectangle cannot be negative (and should be positive, though it could be zero), the practical domain of A is determined when

`50W - W^2\geq 0`

Taking common factor W

`W(50 - W)\geq 0`

Since W must be positive W>0

`50 - W\geq 0`

Or equivalently

`50 \geq W`

`W \leq 50`

The total interval is

`0 < W<50`

Correct option: A

Please note: The real restriction should be

`0 < W\leq 50`

if we allowed the area to be positive, but I'm providing the most possible correct available option