Determine the domain and the range of the function.
-$$f ( x ) = x ^ { 2 } + 12 x$$
A) domain: all real numbers
range: $\{ y \mid y \geq - 36 \}$

B) domain: $\{ x \mid x \geq 6 \}$
range: $\{ y \mid y \geq 36 \}$

C) domain: $\{ x \mid x \geq - 6 \}$
range: $\{ y \mid y \geq - 36 \}$

D) domain: all real numbers
range: $\{ y \mid y \geq 36 \}$

Question

Determine the domain and the range of the function.
-$$f ( x ) = x ^ { 2 } + 12 x$$
A) domain: all real numbers
range: $\{ y \mid y \geq - 36 \}$

B) domain: $\{ x \mid x \geq 6 \}$ 
range: $\{ y \mid y \geq  36 \}$

C) domain: $\{ x \mid x \geq - 6 \}$
range: $\{ y \mid y \geq - 36 \}$

D) domain: all real numbers  
range: $\{ y \mid y \geq 36 \}$

Quizplus · Accepted Answer

The function $f(x) = x^2 + 12x$ is a quadratic function, which is defined for all real numbers, so its domain is all real numbers. Completing the square gives $f(x) = (x + 6)^2 - 36$, showing its vertex at $(-6, -36)$ and indicating the minimum value of $y$ is $-36$, so the range is $\{y \mid y \geq -36\}$.

Determine the Domain and the Range of the Function f(x)=x2+12xf ( x ) = x ^ { 2 } + 12 xf(x)=x2+12x

Determine the Domain and the Range of the Function $f ( x ) = x ^ { 2 } + 12 x$