The function $f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x 0 \end{array} \right\}$ is Select all that apply. A) odd B) even C) neither even nor odd D) continuous on $[ - \pi , \pi ]$ E) discontinuous on $[ - \pi , \pi ]$

Question

The function $f ( x ) = \left\{ \begin{array} { c c } 
x & \text { if } x < 0 \
2 - x & \text { if } x > 0
\end{array} \right\}$ is Select all that apply.
A) odd
B) even
C) neither even nor odd
D) continuous on $[ - \pi , \pi ]$
E) discontinuous on $[ - \pi , \pi ]$

Quizplus · Accepted Answer

The function is neither even nor odd because it does not satisfy the conditions for either: $f(-x) \neq f(x)$ for even functions and $f(-x) \neq -f(x)$ for odd functions, given the piecewise definition. It is discontinuous at $x = 0$ because the function is not defined at $x = 0$, creating a break in the function on the interval $[- \pi , \pi ]$.

The Function f(x)={x if x<02−x if x>0}f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x < 0 \\2 - x & \text { if } x > 0\end{array} \right\}f(x)={x2−x​ if x<0 if x>0​}

The Function $f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x < 0 \\2 - x & \text { if } x > 0\end{array} \right\}$