1. **Linear functions:** These are of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Examples: 1) $y = 2x + 3$ 2) $y = -x + 1$ 2. **Quadratic functions:** These are of the form $y = ax^2 + bx + c$. Examples: 1) $y = x^2 - 4x + 4$ 2) $y = -2x^2 + 3x - 1$ 3. **Absolute value functions:** These are of the form $y = a|bx + c| + d$. Examples: 1) $y = |x - 1|$ 2) $y = 3|2x + 5| - 4$ 4. **Piecewise functions:** Functions defined by different expressions over different intervals. Examples: 1) $y = \begin{cases} x + 2 & x \leq 0 \\ -x + 2 & x > 0 \end{cases}$ 2) $y = \begin{cases} x^2 & x < 1 \\ 3x - 1 & x \geq 1 \end{cases}$ 5. **Cubic functions:** These have the form $y = ax^3 + bx^2 + cx + d$. Examples: 1) $y = x^3 - 3x^2 + 2$ 2) $y = -2x^3 + x + 1$