1. **Linear function:** The general form is $y = mx + c$, where $m$ is the gradient (slope) and $c$ is the y-intercept. 2. **Quadratic function:** The general form is $y = ax^2 + bx + c$. The graph is a parabola that opens upwards (smile) if $a > 0$ and downwards (frown) if $a < 0$. The axis of symmetry is the vertical line given by $x = -\frac{b}{2a}$. 3. **Hyperbola:** The form is $y = \frac{a}{x} + q$. It has vertical asymptote at $x=0$ and horizontal asymptote at $y=q$. 4. **Exponential function:** The form is $y = a \cdot b^x + q$. If $b > 1$, the function shows exponential growth; if $0 < b < 1$, it shows exponential decay. 5. **Transformations:** - Adding or subtracting $q$ shifts the graph vertically by $q$ units. - Replacing $x$ by $(x - p)$ shifts the graph horizontally by $p$ units. - Multiplying by $-a$ reflects the graph across the x-axis if $a$ is positive. These are the key forms and transformations for the requested graphs.