Question

The length of a rectangle is 4 units greater than its width, and the area of the rectangle can be expressed by the equation y=xsquared +4x. What is a resonable domain for this function?

Answer 1

X>0 and y>0 therefore, (0,≈)

Answer 2

The domain of the function is
`D=x|x>0`

Explanation:

Given : The length of a rectangle is 4 units greater than its width, and the area of the rectangle can be expressed by the equation
`y=x^2+4x`

To find : What is a reasonable domain for this function?

Solution :

Domain is defined as the all possible set of values in which function is defined.

We have given the area,

`y=x^2+4x`

We know, Area will never be negative so the value of x is always positive.

So,
`y> 0`

`x^2+4x>0`

`x(x+4)> 0`

i.e. Either
`x>0`

or
`x+4> 0`

`x> -4` but x>0

So, The value of x is defined from 0 to infinity.

The domain of the function is
`D=x|x>0`