Precalculus With Limits: A Graphing Approach →

Identify Amplitude (height), Period (length of one cycle), and Phase Shift (horizontal slide). Identities: Use Pythagorean identities ( ) to simplify expressions before graphing. 5. Limits: The Bridge to Calculus

Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero.

Before graphing complex equations, you must recognize the "parent" functions by sight. (Diagonal line) Quadratic: (U-shaped parabola) Cubic: Absolute Value: Square Root: (Starts at origin, curves right) Reciprocal: (Hyperbola with asymptotes) 2. Understand Transformations Precalculus with Limits: A Graphing Approach

Use the Leading Coefficient Test to see where the graph goes as

These determine the horizontal asymptotes of the graph. 🚀 Study Tips Identify Amplitude (height), Period (length of one cycle),

Master Precalculus with Limits: A Graphing Approach This guide focuses on mastering functions, trigonometry, and the introduction to calculus through a visual and graphical lens. 1. Master the Library of Functions

Use a graphing calculator to verify your hand-drawn sketches, not replace them. Limits: The Bridge to Calculus Find x-intercepts and

Always check for "illegal" math (denominators of zero or negatives in square roots).