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