Question

What is the domain and range of `y=x^2 - 4x + 1`?

Answer 1

Range: `y>=-3`
Domain: `x in RR`

Explanation:

Complete the square (putting the function in vertex form)

`y=(x-2)^2-4+1`
`y=(x-2)^2-3`

Hence the minimum of the function is `y=-3`, so we can say that the range is

`y>=-3`

As for the domain, any value of `x` can be passed to the function so we say that the domain is

`x in RR`