These determine the horizontal asymptotes of the graph. 🚀 Study Tips
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 Precalculus with Limits: A Graphing Approach
Compare the degrees of the numerator and denominator. 4. Trigonometry via the Unit Circle Coordinates: Remember These determine the horizontal asymptotes of the graph
Graphing is easier when you view equations as "shifts" of the parent functions. Horizontal Shifts: (Right) or Reflections: (Over x-axis) or (Over y-axis) Scaling: stretches or shrinks the graph vertically. 3. Analyze Polynomial & Rational Functions Master the Library of Functions Compare the degrees
Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero.
Always check for "illegal" math (denominators of zero or negatives in square roots).
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