3. Plot the graph of the function $y=\frac{x^{2}}{|x|}$.
Answer. See the figure.

Solution. Since $x^{2}=|x|^{2}$, then $y=|x|$, and $x \neq 0$.

We can also, using the definition of the absolute value, obtain that

$$
y=\left\{\begin{array}{l}
x, \text { if } x>0, \\
-x, \text { if } x<0
\end{array} \quad \text { (for } x=0\right. \text { the function is not }
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_6d84e79b533ef6f1310eg-1.jpg?height=494&width=820&top_left_y=1877&top_left_x=1075)

Grading criteria.

- Correct graph with explanation - 7 points.
- Correct graph without any explanation - $\mathbf{5}$ points.
- Graph of the function $y=|x|$ without the punctured point - 3 points.