Question

How do you find the domain and range of `y = x^2 - x + 5`?

Answer 1

The function is a polunomial, so its domain is the whole set of real numbers. `D=RR`.

To find the range we have to look at the formula.

The graph of the function is a parabola. The coefficient of `x^2` is positive, so the parabola goes to `+oo` as the argument goes to
`+-oo`, so the range is `R= < q;+oo)`, where `q` is the `y` coordinate of the vertex.

To calculateit we can first calculate `x` coordinate of the vertex (usually called `p`)

`p=(-b)/(2a)=1/2`

Now we can calculate `q` by substituting `p` to the function's formula:

`q=f(1/2)=(1/2)^2-(1/2)+5=4 3/4`

Now we can write the range:

`R=<4 3/4;+oo)`