Use the Leading Coefficient Test to see where the graph goes as
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 Precalculus with Limits: A Graphing Approach
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 Use the Leading Coefficient Test to see where
Follow the line from both sides; if they meet at the same height, the limit exists. Algebraic View: Try direct substitution first; if you get , factor or rationalize. Period (length of one cycle)
The "Limit" describes the behavior of a function as it approaches a specific point.