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

Question

asked Mar 8, 2021 161k views

1 Answer

Chaya · Answer 1 · 2021-03-12T08:37:51+0000

Answer:

Domain: (-∞,∞) or -∞ <
<∞

Range: [1,∞) or
$y\geq 1$

Explanation:

Given function:

f(x)=x^2-2x+2

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:
f(x)=x^2-2x+2

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 :

h=(-b)/(2a)

Thus, for the function:

h=(-(-2))/(2(1))

h=(2)/(2) [Two negatives multiply to get a positive]

h=1

To find y-coordinate of the vertex can be found out by evaluating
f(h) .

k=f(h)

Thus, for the function:

k=f(1)=(1)^2-2(1)+2

k=f(1)=1-2+2

k=f(1)=1

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

thus, range of the function is:

[1,∞) or
$y\geq 1$