Determine the domain and the range of the function.
-$$f ( x ) = x ^ { 2 } - 12 x + 36$$
A) domain: all real numbers
range: $\{ y \mid y \geq 0 \}$

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

C) domain: $\{ x \mid x \geq - 6 \}$
range: $\{ y \mid y \geq 0 \}$

D) domain: $\{ x \mid x \geq 6 \}$
range: $\left\{ y ^ { \mid } y \geq 0 \right\}$

Question

Determine the domain and the range of the function.
-$$f ( x ) = x ^ { 2 } - 12 x + 36$$
A) domain: all real numbers
range: $\{ y \mid y \geq 0 \}$

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

C) domain: $\{ x \mid x \geq - 6 \}$
range: $\{ y \mid y \geq 0 \}$

D) domain: $\{ x \mid x \geq 6 \}$
range: $\left\{ y ^ { \mid } y \geq 0 \right\}$

Quizplus · Accepted Answer

The function $f(x) = x^2 - 12x + 36$ is a quadratic function, which means its graph is a parabola. The domain of any quadratic function is all real numbers because you can plug any real number into the function and get a real number out. The given function can be rewritten in vertex form as $f(x) = (x-6)^2$, which shows that its vertex is at (6, 0) and it opens upwards. This means the lowest value of $y$ (the range's minimum) is 0, and it increases without bound from there. Therefore, the range is $\{ y \mid y \geq 0 \}$.

Determine the Domain and the Range of the Function f(x)=x2−12x+36f ( x ) = x ^ { 2 } - 12 x + 36f(x)=x2−12x+36

Determine the Domain and the Range of the Function $f ( x ) = x ^ { 2 } - 12 x + 36$