Question

The area of this rectangle is given by the quadratic function

Answer 1

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

Step-by-step 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

$0 < W$

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