Warm Up Let f(x)  5x + 1 and g(x)  √x. a.Is f(g(x)) continuous at x  3? b.Is f(g(x)) continuous at x  0? c.Is g(f(x)) continuous at x  3? d.Is g(f(x))

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Presentation transcript:

Warm Up Let f(x)  5x + 1 and g(x)  √x. a.Is f(g(x)) continuous at x  3? b.Is f(g(x)) continuous at x  0? c.Is g(f(x)) continuous at x  3? d.Is g(f(x)) continuous at x  0?

Homework: Packet pg. 6 1.Y, Y, Y, N 2.Y, Y, N, N 3.N, N 4.(-1, 0)  (0, 1)  (1, 2)  (2, 3) 5.f(2)  0 6.f(1)  2 7.No, the graph as a jump discontinuity at 0. 8.Yes, If we extend the function y  0 to end at x  4.

Test Format 2 Free Response - 1 No Calculator 5 parts (15 minutes) - 1 Calculator 4 parts (15 minutes) 18 Multiple Choice - 11 No Calculator (22 minutes) - 7 Calculator (21 minutes)

AP Calculus AB Infinite Limits Vertical Asymptotes VideoVideo Part 1

Infinite Limit- f(x) increases or decreases without bound. Means that while the limit FAILS TO EXIST, the function will increase without bound.

Vertical Asymptote The line x = a is a vertical asymptote of the graph of a function y = f(x) if either

THM: Anytime you get a nonzero number over zero, there is a vertical asymptote at that x value. EX/

BUT, a vertical asymptote DOES NOT guarantee the limit exists

Properties of infinite limits:

Practice:

More Practice…

Video Segment 2 & 3

So… Bottom degree bigger Same degree Top degree bigger limit = 0 limit = # (the ratio of coefficients) + or - infinitiy

End Behavior Models Same rules as Horizontal Asymptotes Algebraically: Divide by highest degree of the denominator.

Practice:

Limits of Composite Functions f(x)g(x) 1. What is ? 2. What is

Video Segment 4

Practice

Packet pg. 8 & 9