$\text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. }$
A) domain: $[ - 6 , \infty )$
range: $[ - 6 , \infty )$
B) domain: $[ - 6 , \infty )$
range: $( - 6 , \infty )$
C) domain: $( - \infty , \infty )$
range: $( - 6 , \infty )$
D) domain: $( - \infty , \infty )$
range: $[ 6 , \infty )$
E) domain: $( - \infty , \infty )$
range: $[ - 6 , \infty )$

Question

$\text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. }$ 
A) domain: $[ - 6 , \infty )$
range: $[ - 6 , \infty )$
B) domain: $[ - 6 , \infty )$
range: $( - 6 , \infty )$
C) domain: $( - \infty , \infty )$
range: $( - 6 , \infty )$
D) domain: $( - \infty , \infty )$
range: $[ 6 , \infty )$
E) domain: $( - \infty , \infty )$
range: $[ - 6 , \infty )$

Quizplus · Accepted Answer

The function $f(x) = x^2 - 6$ is a quadratic function, where $x$ can take any real value, hence its domain is $(-\infty, \infty)$. The vertex of this parabola is at $(0, -6)$, making $-6$ the minimum value of $f(x)$, so the range is $[ - 6 , \infty )$.

Find the domain and range of the function f(x)=x2−6. \text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. } Find the domain and range of the function f(x)=x2−6.

$\text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. }$