Precalculus With Limits: A Graphing Approach – Updated

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

Compare the degrees of the numerator and denominator. 4. Trigonometry via the Unit Circle Coordinates: Remember Precalculus with Limits: A Graphing Approach

If a graph looks weird, plot 3-5 specific points to anchor it. Always check for "illegal" math (denominators of zero

Use a graphing calculator to verify your hand-drawn sketches, not replace them. if you get

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.

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