No class Monday with Labor Day. Went over homework in DS, then learned how to make a piecewise function continuous by using the definition of continuity. Warm up in class took this idea further, as it involved solving a system of equations to find the constants to make the function continuous. Then looked at the Intermediate Value Theorem and how it can be used to guarantee the existence of roots in an interval when dealing with continuous functions (this is the first part of our "formulas and theorems" booklet used throughout the year). Worked through 2 examples of writing with the IVT and then introduced EVT and figured out what it says. Started working on AP practice problems in groups, these will be continued Friday if I survive the dentist -_-
Notes from board
Homework
Start working on the limits packet, due Wednesday 9/13 [blank copy]
Study for assessment on Friday in class:
- given absolute value function, find limit (involves writing as piecewise)
- given piecewise function, show if it is or is not continuous at a point
- find the values of constants to make a function continuous (will not involve system of equations this time)
- find and classify discontinuities, justify with limits
Resources
finding a and b to make piecewise function continuous, NOT involving system: link
finding a and b to make piecewise function continuous, involving system: link
Using IVT to show existence of root in a given interval: link
Assessment study resources
absolute value limit: link1 link2
determine if piecewise function is continuous or not using def of continuity: link
finding a and b to make piecewise function continuous, NOT involving system: link
find and classify discontinuities, justify with limits: link