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Students will be able to write a comprehensible and reasonable piecewise function that has either four or five pieces.
Students will be able to identify discontinuities on their piecewise graph and write the appropriate one-sided limit statements.
Students will be able to identify the intervals of continuity on their graph.
Students will be able to describe key facts about their graph outside of the limit statments
Students will write and graph their own four-piece and five-piece piecewise functions with the given specifications.
Write and graph your own 4 piece piecewise graph!
1. Constant function
2. Linear function
3. Quadratic Function
4. Square root function (make sure your function exists in your boundary values)
Pick boundaries for each graph. Make sure they won't make your graph go to high or low on the graph
Write the one-sided limit statements for each of the jump discontinuities
*NEW* Write the value of the function at each of the jump discontinuities
Write the intervals on which your graph is continuous
Write at least THREE (not two!) pieces of other information from your graph (number/type of discontinuities, values, etc... be as "HOT" as possible - don't be simple!)
Write and graph your own 4 piece piecewise graph!
1. Linear function
2. Logarithmic function (make sure your function exists in your boundary values)
3. Exponential Function (make sure your function reasonably exists in your boundary values)
4. Cubic function (make sure your function reasonably exists in your boundary values)
5. Rational Function (make sure your function exists in your boundary values)
Pick boundaries for each graph. Make sure they won't make your graph go to high or low on the graph
Write the one-sided limit statements for each of the jump discontinuities. You must include BOTH jump and infinite discontinuities, so plan your graphs accordingly.
*NEW* Write the value of the function at each of the jump discontinuities
Write the intervals on which your graph is continuous
Write at least THREE (not two!) pieces of other information from your graph (number/type of discontinuities, values, etc... be as "HOT" as possible - don't be simple!)
*Challenge: Make one of your "change in function" points STILL BE CONTINUOUS!
