What are the domain and range of #f(x)=x^2-2x+3#?

1 Answer
Daniel L.
Jan 1, 2017

See explanation.

Explanation:

Domain

The domain of a function is the largest subset of #RR# for which the function's formula is defined.

Given function is a polynomial, so there are no limitations for the values of #x#. This means that the domain is #D=RR#

Range

The range is the interval of values which a function takes.

A quadratic function with a positive coefficient of #x^2# takes all values in an interval #[q;+oo)# where #q# is the #y# coefficient of the function's vertex.

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

#q=f(p)=1^2-2*1+3=1-2+3=2#

The function's range is #[2;+oo)#

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