```markdown
### Quasiconvex Functions

- **Definition**: A function \( f : \mathbb{R}^n \to \mathbb{R} \) is quasiconvex if \( \text{dom} \, f \) is convex and the sublevel sets 
  \[
  S_\alpha = \{ x \in \text{dom} \, f \mid f(x) \leq \alpha \}
  \]
  are convex for all \( \alpha \).

- **Graph Description**: The graph shows a curve with two horizontal dashed lines labeled \( \alpha \) and \( \beta \). The curve intersects the \( \alpha \) line at two points, labeled \( a \) and \( b \), and continues upward past the \( \beta \) line at point \( c \).

- **Additional Notes**:
  - \( f \) is quasiconcave if \(-f\) is quasiconvex.
  - \( f \) is quasilinear if it is both quasiconvex and quasiconcave.

- **Source**: A. d’Aspremont. Convex Optimization M2.
```
