Question

How do you find the domain and range of `Y=-x^2+4x-1`?

Answer 1

See explanation.

Explanation:

The function is a polynomial, so it is defined for all real values of `x`. This means that the domian is `D=RR`

To calculate the range we have to find the vertex of the parabola:

`p=(-b)/(2a)=(-4)/-2=2`

`q=f(p)=-2^2+4*2-1=3`
graph{-x^2+4x-1 [-11.25, 11.25, -5.625, 5.625]}

From the graph we see that the range is `(-oo;3]`