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: $( - \infty , - 2 )$; range: $( - \infty , \infty )$
D) Domain: $( - \infty , \infty )$; range: $( - \infty , - 2 )$

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 form of the function shows that the minimum value of $f(x)$ is $-2$, achieved when $x = -2$, and the function opens upwards.

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 $f ( x ) = ( x + 2 ) ^ { 2 } - 2$