26 – Limits and Continuity II – Day 1 No Calculator

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26 – Limits and Continuity II – Day 1 No Calculator Rational Function Investigations 26 – Limits and Continuity II – Day 1 No Calculator

Limit – the intended height of a function continuous at x = –4 point discontinuity at x = 0 jump discontinuity at x = 2

infinite discontinuity at x = –3 When does this happen algebraically?

A denominator can never be zero. Therefore…. Rational Function – A quotient of polynomials such that the denominator has a degree of at least 1. A denominator can never be zero. Therefore…. f(x) is discontinuous at x = –2 and x = –3 g(x) is discontinuous at x = –1 and x = –3 h(x) is discontinuous at x = 2 and x = –1 What type of discontinuity exists?

f(x) is discontinuous at x = –2 and x = –3 Any limit resulting in indicates a point discontinuity. f(x) is discontinuous at x = –2 and x = –3 There is a point discontinuity at (–2, 1). There is a hole in the graph at (–2, 1).

f(x) is discontinuous at x = –2 and x = –3 Any limit resulting in indicates an infinite discontinuity. There is a vertical asymptote in the graph at x = –3. To determine the behavior of the graph, we substitute values close to x = –3 on each side. f(x) is discontinuous at x = –2 and x = –3

infinite discontinuity point discontinuity vertical asymptote at x = –1 hole at g(x) is discontinuous at x = –1 and x = –3

infinite discontinuity point discontinuity vertical asymptote at x = 2 hole at h(x) is discontinuous at x = 2 and x = –1

infinite discontinuity at x = –4 9. Determine where is discontinuous. Find the type of each discontinuity. infinite discontinuity at x = –4 vertical asymptote at x = –4 Behavior of graph…..

infinite discontinuity at x = 2 10. Determine where is discontinuous. Find the type of each discontinuity. infinite discontinuity at x = 2 vertical asymptote at x = 2 Behavior of graph…..

infinite discontinuity 11. Determine where is discontinuous. Find the type of each discontinuity. infinite discontinuity vertical asymptote at x = –1 Behavior of graph…..

Find the type of each discontinuity. 12. Determine where is discontinuous. Find the type of each discontinuity. point discontinuity at x = 3 infinite discontinuity at x = –1 vertical asymptote at x = –1 hole at

Find the type of each discontinuity. 13. Determine where is discontinuous. Find the type of each discontinuity. point discontinuity at x = –3 infinite discontinuity at x = 1 vertical asymptote at x = 1 hole at