Anna and Emma were getting ready for their math test. Anna was explaining the properties of a function to Emma. To illustrate her statements, she used her own graph of a function $f$:
Anna claimed:
(1) The domain of the function $f$ is the interval $[ -6;10 ]$.
(2) The function $f$ is not one-to-one.
(3) The function $f$ is odd.
(4) The function $f$ is bounded.
Did Anna make any mistake? If yes, specify where.
Yes, Anna made a mistake in point (1).
Yes, Anna made a mistake in point (2).
Yes, Anna made a mistake in point (3).
Yes, Anna made a mistake in point (4).
No, Anna did not make a mistake.
A function $f$ is odd if, for every $x$ from the domain of $f$, $-x$ is also in the domain of $f$, and, moreover, the equality $f(x)=-f(-x)$ holds for all $x$ from the domain of $f$.
As we can see from the graph of $f$, the domain of $f$ is not "symmetric". For example, the number $8$ belongs to the domain, but $-8$ does not. Therefore, the function $f$ is not odd.
