Find the domain and range of the function.
-$$f ( x ) = 3 x ^ { 2 } - 42 x + 151$$
A) Domain: $( - \infty , \infty )$; Range: $[ 4 , \infty )$
B) Domain: $( - \infty , \infty )$; Range: $[ 0 , \infty )$
C) Domain: $( - \infty , \infty )$; Range: $( - \infty , 0 ]$
D) Domain: $( - \infty , \infty )$; Range: $( - \infty , 7 ]$

Question

Quizplus · Accepted Answer

The domain of any quadratic function is $(- \infty , \infty )$ because you can input any real number for $x$. To find the range, first find the vertex of the parabola. The vertex formula is $(-b/2a, f(-b/2a))$. For $f(x) = 3x^2 - 42x + 151$, $a = 3$, $b = -42$, so $-b/2a = 7$. Plugging $x = 7$ into $f(x)$ gives the minimum value of the function, which is $f(7) = 3(7)^2 - 42(7) + 151 = 4$. Since it's a parabola opening upwards (a > 0), the range is $[4, \infty)$.

Find the Domain and Range of the Function f(x)=3x2−42x+151f ( x ) = 3 x ^ { 2 } - 42 x + 151f(x)=3x2−42x+151

Find the Domain and Range of the Function $f ( x ) = 3 x ^ { 2 } - 42 x + 151$