Question

How do you find the domain and range of `f(t) = 3sqrt(t + 4)`?

Answer 1

Assuming we are restricted to Real values:
Domain: `t in [-4,+oo)`
Range:`f(t) in [0,+oo)`

Explanation:

`3sqrt(t+4)` is only defined (in Real values) if `t+4>=0`
`rArr t>=-4`
however, it is defined for all `t >= -4`;
therefore the Domain is `t >=-4 or t in [-4,+oo)`

`sqrt(t+4) >= 0` (by definition of the square root function)
It is equal to `0` when `t=-4`
As `trarr+oo`
`color(white)("XXX")sqrt(t+4)rarr +oo` (and so does `3sqrt(t+4)`)
Therefore the Range is `f(t) > 0 or f(t) in [0,+oo)`