Continuous Graphs, Jumps and Holes Worksheet with Answer Key

What's on the worksheet

1. Use each table near x equal to 2 to say if the graph is unbroken or broken, and how.
2. List every input where the graph is broken and name the kind of break.
3. Find every break in each function, giving holes as points and asymptotes as lines.
   y = \dfrac{x^2 - 5x}{25 - x^2}y = \dfrac{x^3 - 4x}{x^2 + 2x}y = \dfrac{x^2 - 3x}{x^3 - 6x^2 + 9x}
4. Word problem: the height of a playground slide described by a piecewise rule.
5. Find a and b so the piecewise graph is unbroken everywhere.
6. Show a polynomial has a zero between two inputs, and test the same idea on a rational function.
7. Decide whether each statement about breaks is always true, with a reason or counterexample.