```markdown
### Examples of Quasiconvex and Quasilinear Functions

- **Quasiconvex Function**: 
  - \( \sqrt{|x|} \) is quasiconvex on \( \mathbb{R} \).

- **Quasilinear Function**: 
  - \( \text{ceil}(x) = \inf\{z \in \mathbb{Z} \mid z \geq x\} \) is quasilinear.
  - \( \log x \) is quasilinear on \( \mathbb{R}_{++} \).

- **Quasiconcave Function**: 
  - \( f(x_1, x_2) = x_1 x_2 \) is quasiconcave on \( \mathbb{R}^2_{++} \).

- **Linear-Fractional Function**: 
  - \( f(x) = \frac{a^T x + b}{c^T x + d} \), where \( \text{dom } f = \{x \mid c^T x + d > 0\} \), is quasilinear.

- **Distance Ratio**: 
  - \( f(x) = \frac{\|x - a\|_2}{\|x - b\|_2} \), where \( \text{dom } f = \{x \mid \|x - a\|_2 \leq \|x - b\|_2\} \), is quasiconvex.
```
