Question

How do you find the domain and range for `F(x) = 6x^2 - 2x +7`?

Answer 1

Domain is `RR`, range is `<6 5/6;+oo)`

This function is a polynomial, so its domain is whole set `RR`.

To find the range you have to see, that the coefficient next to `x^2` is positive, so the graph is going to `+oo` as the argument `x` goes to `-oo` or `+oo`, so the range can be written as
`< q;+oo)` where `q=f(p)` and `p=-b/(2a)`

`p=2/12=1/6`
`q=f(1/6)=6*(1/6)^2-2*1/6+7=1/6-2/6+7=-1/6+7=6 5/6`