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

1 Answer
May 28, 2017

Answer:

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]#