After the mathematics class, there was a graph of a linear-to-linear rational function $f$ left on the board.
Students who entered the classroom discussed the properties of this function. Gradually, they agreed on:
The function $f$ is decreasing on $\left(-\infty,3\right)\cup\left(3,\infty\right)$.
The function $f$ is neither odd nor even.
Function $f$ is a one-to-one function.
The range of the function $f$ is all non-zero real numbers.
Did they make any mistakes? If yes, determine where:
Yes, at point 1.
Yes, at point 2.
Yes, at point 3.
Yes, at point 4.
No, all statements are true.
The given function $f$ is decreasing on the interval $\left(-\infty,3\right)$ and on the interval $\left(3,\infty\right)$. However, it is not decreasing on the union of these intervals. It is sufficient to realize, for example, that, $f\left(2\right) < f\left(4\right)$.
