Question

Given the piecewise function `y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4`, how do you find the domain?

Answer 1

The Domain is the set of all values of `x` fro which the function is defined; in this case the domain is `[-4,+4]`

Explanation:

Given
`color(white)("XX")y = {(sqrt(-x)" for "-4 <= x <=0), (sqrt(x)" for "0 < x <=4)}`

The first element of this set definition defines the function for all values of `x in [-4,0]`

The second element in this set definition defines the function for all values of `x in (0,+4]`

Togheter they define the function for all values of `x in [-4,+4]`