Question

What is the range of the function `2(x-3)^2+1`?

Answer 1

Range: `f(x) in [1,+oo)`

Explanation:

Note that `(x-3)^2` has a minimum value of `color(blue)0`
in which case `2(x-3)^2+1` has a value of `color(red)1`

Also note that `(x-3)^2` has no upper limit
so as the value of `(x-3)^2` increases `2(x-3)^2+1 rarr +oo`