Understanding Function Graphing
Graphing a function means representing the set of all ordered pairs (x, y) satisfying y = f(x) on a 2D Cartesian plane.
The 4 Universal Graphing Steps
- Find Intercepts: Set x = 0 for the Y-intercept; set y = 0 for the X-intercepts.
- Identify Asymptotes: Look for vertical asymptotes where the denominator equals zero, and horizontal asymptotes as x → ∞.
- Create a Table of Values: Choose key X-values surrounding domain boundaries and calculate their corresponding Y-outputs.
- Plot Points & Draw Curve: Connect points smoothly according to the function's family behavior (linear, parabolic, or asymptotic).