Question

Given no other restrictions, what are the domain and range of the following funtction? f(x)=x^2-2x+2

Answer 1

Answer: Domain of the given function is all real numbers.

Range of the given function is {y | y>=1}

Step-by-step explanation:

The given function is a polynomial and the domain of any polynomial is all the real numbers because for any value of x, the function will have some value.

Hence, the domain will be all real numbers.

Range is the set of y values for which the function is defined.

This is a polynomial and to find the range, we will simplify the polynomial.

$f(x)=x^2-2x+2\\f(x)=(x-1)^2+1$

Therefore, for any value of x, f(x) ≥ 1

Hence, the range becomes {y | y ≥ 1}

Answer 2

F ( x ) = x² - 2 x + 2
The vertex form:
f ( x ) = ( x² - 2 x + 1 )- 1 + 2 = ( x - 1 )² + 1
Coordinates of the vertex are:  ( 1 , 1 ).
Domain:  x ∈ R
Range:  x ∈ [ 1. + ∞ )