Question

What is the domain and range of `y=sqrt(5x+2)`?

Answer 1

`x>= -2/5, x inRR`
`y>=0, y in RR`

Explanation:

The domain is the values of `x` for which we can plot a value for `y`.
We cannot plot a value for `y` if the area under the square root sign is negative since you cannot take the square root of a negative (and get a real answer.
To give us the domain:

let `5x+2>=0`
`5x>= -2`
`x>= -2/5, x inRR`

The range is the values of `y` we get from plotting this function.
We get our lowest value when `x=-2/5`

Let `x=-2/5`
`y=sqrt(5(-2/5)+2`
`y=sqrt(-2+2)`

`y=sqrt0=0`
Any x value greater than -2/5 will give a bigger answer, and as `x-> oo, y-> oo` also.

So the range is `y>=0, y in RR`