Find the domain and range of the function.
-$$f ( x ) = ( x - 2 ) ^ { 2 } + 2$$
A) Domain: $( - 2 , \infty )$; range: $( - \infty , \infty )$
B) Domain: $( - \infty , \infty )$; range: $[ 2 , \infty )$
C) Domain: $( - \infty , \infty )$; range: $( - \infty , 2 )$
D) Domain: $( - \infty , 2 )$; range: $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The domain of a quadratic function is always $( - \infty , \infty )$ because you can input any real number into the function. The range is $[ 2 , \infty )$ because the vertex of the parabola is at $(2, 2)$ and it opens upwards, meaning the lowest value of $f(x)$ is 2, and it increases without bound from there.

Find the Domain and Range of the Function f(x)=(x−2)2+2f ( x ) = ( x - 2 ) ^ { 2 } + 2f(x)=(x−2)2+2

Find the Domain and Range of the Function $f ( x ) = ( x - 2 ) ^ { 2 } + 2$