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Precalculus With Limits: A Graphing Approach -

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

The "Limit" describes the behavior of a function as it approaches a specific point. Precalculus with Limits: A Graphing Approach

If a graph looks weird, plot 3-5 specific points to anchor it. Use a graphing calculator to verify your hand-drawn

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 Graphing is easier when you view equations as

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