1. Practice! 1. For the graph shown, which of these statements is FALSE? (A) f(x) is continuous at x=2 (B) (C) (D) (E) f(x) is continuous everywhere from 2.

2. AP Calculus Unit 1 Day 7 Continuity, Composition, & Intermediate Value Theorem

3. Three Types of Discontinuity—Be Familiar with the Vocabulary 1.Hole when factors divide out “Removable discontinuity” 2.Asymptotes when denominator = 0 “Infinite discontinuity, nonremovable” 3.Piecewise Graph or Greatest Integer Function “Jump Discontinuity, also nonremovable”

4. f(x) is continuous at x=c if... Official Definition Which means...

5. Is f(x) continuous at x = 4? Justify your answer

6. Is f(x) continuous at x = 3? Justify your answer

7. “Remove” the discontinuity in this function by rewriting the function as a piecewise function.

8. Intermediate Value Thm. A continuous function takes on all y values between f(a) and f(b). As Related to The Preview Video If W is between f(a) & f(b), then W = f(c) for some c in [a,b]

9. Graphical Illustration of the Intermediate Value Theorem a b f(b) f(a) Any W value in here will be “hit” at least once

10. Intermediate Value Theorem in Action Given f(x) is continuous on the interval [0,4]. What is the minimum number of times f(x) = 8? Justify. x01234 f(x)106279

11. Composition of functions

12. Composition of functions... Is f(g(x)) continuous at x = 4?

13. We must evaluate Therefore f(g(x)) is continuous

15. Find the limit of the composition