The "Limit" describes the behavior of a function as it approaches a specific point.
Use a graphing calculator to verify your hand-drawn sketches, not replace them. Precalculus with Limits: A Graphing Approach
Use the Leading Coefficient Test to see where the graph goes as The "Limit" describes the behavior of a function
Always check for "illegal" math (denominators of zero or negatives in square roots). Precalculus with Limits: A Graphing Approach