 Math in the Real World Discussion
 Grades based on tests
 Challenging yourself
 Asking questions in class
Bell Ringer
Find if . 0 undefined 5 5 none of the above
Find if . undefined 14x 14x 14x  9 none of the above
Find the xvalues (if any) at which is not continuous. f(x) is continuous for all real x. f(x) is not continuous at x = 0, –5 and both the discontinuities are nonremovable. f(x) is not continuous only at x = –5 and f(x) has a removable discontinuity at x = –5 . f(x) is not continuous only at x = 0 and f(x) has a removable discontinuity at x = 0 . f(x) is not continuous at x = 0, –5 and f(x) has a removable discontinuity at x = 0 .
Find the xvalues (if any) at which the function is not continuous. Which of the discontinuities are removable? no points of discontinuity. x = –10 (not removable), x = 3 (removable) x = –10 (removable), x = 3 (not removable) no points of continuity. x = –10 (not removable), x = 3 (not removable)
Find the limit (if it exists). 1 / 14 0 1 / 98 1 / 14  limits does not exist
Review
 Math Overview (video)
 Numbers
 Relationships
 Shapes
 Change
 Limits
 Intro to Limits (video)
 Nonexistent Limits (video)
 How are limits found numerically and graphically? (checkpoints)
 How are limits found algebraically? (checkpoints)
Lesson
 Challenge 3
 Find a that makes the following function continuous.
 Find the following limit:
 Graph
 Continuity (video) and Onesided Limits (video)
Exit Ticket
 Posted on the board at the end of the block
Homework WNQ
 Last section of Unit 1
 Lesson Objectives
 How can discontinuity of a function be described?
 How are onesided limits related to regular limits?
Standard(s)
 APC.2
 Define and apply the properties of limits of functions.
 Limits will be evaluated graphically and algebraically.
 Includes:
 limits of a constant
 limits of a sum, product, and quotient
 onesided limits
 limits at infinity, infinite limits, and nonexistent limits*
 APC.3
 Use limits to define continuity and determine where a function is continuous or discontinuous.
 Includes:
 continuity in terms of limits
 continuity at a point and over a closed interval
 application of the Intermediate Value Theorem and the Extreme Value Theorem
 geometric understanding and interpretation of continuity and discontinuity
