Find the range of the function $f ( x ) = \left\{ \begin{array} { l l }
x ^ { 2 } - 4 x & \text { if } x \leq 2 \
| x - 4 | & \text { if } x 2
\end{array} \right.$ .
A)[0,$\infty$).
B)(-$\infty$,2]
C)[-4, $\infty$).
D)(-$\infty$, 0]
E)[4, $\infty$)
F)(-$\infty$,4]
G)[2, $\infty$)
H)(-$\infty$,4] .

Question

Find the range of the function $f ( x ) = \left\{ \begin{array} { l l } 
x ^ { 2 } - 4 x & \text { if } x \leq 2 \
| x - 4 | & \text { if } x > 2
\end{array} \right.$ .
A)[0,$\infty$).
B)(-$\infty$,2]
C)[-4, $\infty$).
D)(-$\infty$, 0]
E)[4, $\infty$)
F)(-$\infty$,4]
G)[2, $\infty$)
H)(-$\infty$,4] .

Quizplus · Accepted Answer

For $x \leq 2$, the function $f(x) = x^2 - 4x$ is a parabola opening upwards with its vertex at $x = 2$, giving the minimum value of $f(2) = 2^2 - 4*2 = -4$. For $x > 2$, the function $f(x) = |x - 4|$ is non-negative and reaches a minimum of 0 when $x = 4$. Thus, the range of the entire function is $[-4, \infty)$.

Find the Range of the Function f(x)={x2−4x if x≤2∣x−4∣ if x>2f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 4 x & \text { if } x \leq 2 \\| x - 4 | & \text { if } x > 2\end{array} \right.f(x)={x2−4x∣x−4∣​ if x≤2 if x>2​

Find the Range of the Function $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 4 x & \text { if } x \leq 2 \\| x - 4 | & \text { if } x > 2\end{array} \right.$