Find domain and range for f(x)=x^2-2x+2

Domain: (-∞,∞) or  -∞ <<∞

Range: [1,∞) or

Step-by-step explanation:

Given function:

To find range and domain of the function.

Solution:

The given function is a second degree function as the highest exponent of the variable is 2. Thus, it is a quadratic function.

For all quadratic functions the domain is a set of all real numbers. So, the domain can be given as: (-∞,∞) or  -∞ <<∞

In order to find the range of the quadratic function, we will first determine if the function has a minimum point or the maximum point.

For a quadratic equation :

1) If the function will have a minimum point.

2) If   the function will have a maximum point.

For the given function:

which is greater than 0, and hence it will have a minimum point.

To find the range we will find the coordinates of the minimum point or the vertex of the function.

The x-coordinate of the vertex of a quadratic function is given by :

Thus, for the function:

 [Two negatives multiply to get a positive]

To find y-coordinate of the vertex can be found out by evaluating .

Thus, for the function:

Thus, the minimum point of the function is at (1,1).

thus, range of the function is:

[1,∞) or

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