Find the range of the function. $f ( x ) = 2 x ^ { 2 } - 3$
A) $[ 0 , \infty )$
B) $(-\infty, \infty)$

C) $( - 3 / 2 , \infty )$
D) $( - \infty , - 3 ) \cup ( 3 , \infty )$
E) $[ - 3 , \infty )$

Question

Find the range of the function. $f ( x ) = 2 x ^ { 2 } - 3$
A) $[ 0 , \infty )$
B) $(-\infty, \infty)$

C) $( - 3 / 2 , \infty )$
D) $( - \infty , - 3 ) \cup ( 3 , \infty )$
E) $[ - 3 , \infty )$

Quizplus · Accepted Answer

To find the range, we need to consider what values the function can output for all possible inputs. Since the coefficient of the squared term is positive, we know that the parabola opens upwards and has a minimum value. To find the minimum value, we can use the formula for the axis of symmetry, which is given by $x = -b/2a$. In this case, $a = 2$, $b=0$, so the axis of symmetry is at $x=0$. Plugging this value into the function, we get $f(0) = -3$. Therefore, the minimum value of the function is $-3$, and all values greater than or equal to $-3$ can be achieved by choosing an appropriate value of $x$. Thus, the range is $[-3,\infty)$. Choice E is the only one that includes this range.

Find the Range of the Function f(x)=2x2−3f ( x ) = 2 x ^ { 2 } - 3f(x)=2x2−3

Find the Range of the Function $f ( x ) = 2 x ^ { 2 } - 3$