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
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 Precalculus with Limits: A Graphing Approach
Compare the degrees of the numerator and denominator. 4. Trigonometry via the Unit Circle Coordinates: Remember Identify Amplitude (height), Period (length of one cycle),
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 Limits: The Bridge to Calculus Before graphing complex
If a graph looks weird, plot 3-5 specific points to anchor it.