Precalculus With Limits: A Graphing Approach ✦

If a graph looks weird, plot 3-5 specific points to anchor it.

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. Precalculus with Limits: A Graphing Approach

Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero. If a graph looks weird, plot 3-5 specific

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 3. Analyze Polynomial & Rational Functions

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

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