Use a graphing calculator to verify your hand-drawn sketches, not replace them.
If a graph looks weird, plot 3-5 specific points to anchor it. Precalculus with Limits: A Graphing Approach
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 Use a graphing calculator to verify your hand-drawn
The "Limit" describes the behavior of a function as it approaches a specific point. Horizontal Shifts: (Right) or Reflections: (Over x-axis) or
Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero.
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