Find the domain and range of the function.
$f ( x ) = x ^ { 2 } + 2 x - 4$
A) $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ - 5 , \infty )$
B) $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ - 1 , \infty )$
C) $\text { Domain: } [ - 5 , \infty ) \text {; Range: } ( - \infty , - 1 ]$
D) $\text { Domain: } [ - 5 , \infty ) \text {; Range: } ( - \infty , 0 ]$

Question

Quizplus · Accepted Answer

The domain of a quadratic function is all real numbers $(- \infty , \infty)$ because there are no restrictions on the values that $x$ can take. To find the range, we complete the square to find the vertex form of the function: $f(x) = (x+1)^2 - 5$. The vertex $(-1, -5)$ shows the minimum value of the function is $-5$, so the range is $[-5, \infty)$.

Find the Domain and Range of the Function f(x)=x2+2x−4f ( x ) = x ^ { 2 } + 2 x - 4f(x)=x2+2x−4

Find the Domain and Range of the Function $f ( x ) = x ^ { 2 } + 2 x - 4$