Question

How do you find the domain and range for `y=sqrt(x+4)`?

Answer 1

Domain: `x>=(-4)` (could also be written as: `x in[-4,+oo)` )
Range: `y>=0` could also be written as: `y in [0,+oo)` )

Explanation:

To determine the domain we need to ask:
`color(white)("XXX")`For what values of `x` is `sqrt(x+4)` valid?

We know that `sqrt("something")` is valid if and only if `"something" >=0` (assuming we are restricted to Real numbers).

Therefore `(x+4)` must be `>=0`
`rArr x>=-4`

To determine the range we need to ask:
`color(white)("XXX")`What values can be generated using legal values of `x` by the expression `sqrt(x+4)`

When `x=-4`
`color(white)("XXX")sqrt(x+4)=0`
When `x> -4`
`color(white)("XXX")sqrt(x+4)>0` with no upper limit as `xrarr+oo`