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These determine the horizontal asymptotes of the graph. 🚀 Study Tips
Use a graphing calculator to verify your hand-drawn sketches, not replace them. Precalculus with Limits: A Graphing Approach
Always check for "illegal" math (denominators of zero or negatives in square roots). These determine the horizontal asymptotes of the graph
Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero. 3. Analyze Polynomial & Rational Functions
Before graphing complex equations, you must recognize the "parent" functions by sight. (Diagonal line) Quadratic: (U-shaped parabola) Cubic: Absolute Value: Square Root: (Starts at origin, curves right) Reciprocal: (Hyperbola with asymptotes) 2. Understand Transformations
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
