Unit 6 – Fundamentals of Calculus

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Unit 6 – Fundamentals of Calculus Section 6

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Presentation transcript:

Unit 6 – Fundamentals of Calculus Section 6.3 – Continuity No Calculator

A function f(x) is continuous at x = c if and only if all three of the following tests hold: f(x) is right continuous at x = -5 f(x) is continuous at x = -4 f(x) has infinite discontinuity at x = -3 f(x) has point discontinuity at x = -2 f(x) has infinite discontinuity at x = -1 f(x) is continuous at x = 0

Point Discontinuity Jump Discontinuity Continuous Continuous At x = 1 At x = 2 At x = 3 At x = 4 At x = 5 Point Discontinuity Jump Discontinuity Continuous Continuous Point Discontinuity

continuous continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 continuous inf. discontinuity at x = -3 jump discontinuity at x = 2

Find the value of a which makes the function below continuous

Find (a, b) which makes the function below continuous As we approach x = -1 2 = -a + b As we approach x = 3 -2 = 3a + b