Precalculus With Limits: A Graphing Approach -

Compare the degrees of the numerator and denominator. 4. Trigonometry via the Unit Circle Coordinates: Remember

Find x-intercepts and determine "multiplicity" (does the graph cross or bounce?). Asymptotes: Vertical: Where the denominator equals zero. Precalculus with Limits: A Graphing Approach

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. Compare the degrees of the numerator and denominator

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 if you get