Linear Fractional (Rational) Function and Its Graph
🎯 Learning Objectives
- Understand what a linear fractional function is and its standard form
- Identify vertical and horizontal asymptotes
- Graph a hyperbola and understand its key features
- Apply transformations to the parent function $y = \frac{1}{x}$
📐 The Parent Function: $y = \frac{1}{x}$
Before we dive into the general form, let's start with the simplest rational function:
$$y = \frac{1}{x}$$
This function is defined for all $x \neq 0$. Its graph is called a hyperbola — a curve with two separate branches.
| $x$ | $y = \frac{1}{x}$ |
|---|---|
| $-4$ | $-0.25$ |
| $-2$ | $-0.5$ |
| $-1$ | $-1$ |
| $-0.5$ | $-2$ |
| $0.5$ | $2$ |
| $1$ | $1$ |
| $2$ | $0.5$ |
| $4$ | $0.25$ |
Interactive visualization — available in the full lesson