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Understanding Continuous Functions and Discontinuities in Precalculus

Learn about continuous functions, removable and jump discontinuities, and infinite discontinuities. Identify and define these concepts for a comprehensive grasp of precalculus. Homework worksheet provided. Bring your calculators for Monday's class.

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Understanding Continuous Functions and Discontinuities in Precalculus

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  1. Today in Precalculus • Quiz until 1:20 • When you are done, turn it in and sit quietly. • Notes: (no handout) • Define and Identify a Continuous function • Name and Identify types of discontinuity • Homework • Bring calculators Monday

  2. Continuous Functions • Definition: A function where the graph does not come apart at any point on its domain. It is continuous everywhere on its domain.

  3. Removable Discontinuity • This graph is continuous everywhere except for the hole at x = 1.5 • This is called a removable discontinuity because it can be patched by redefining f(1.5) so as to plug the hole.

  4. Removable Discontinuity • This graph also has a removable discontinuity • This is removable because we could define f(1.5) so as to plug the hole and make f continuous at f(1.5).

  5. Jump Discontinuity • This discontinuity is not removable because there is more than just a hole at x = -2. • It is a Jump Discontinuity because there is more than a hole, there is a jump in the function values that makes it impossible to plug with a single point.

  6. Infinite Discontinuity • This discontinuity is not removable because there is more than just a hole at x = -1. • It is a Infinite Discontinuity at x = -1 because the two sides are approaching infinity.

  7. Practice Continuous Discontinuous- Infinite Discontinuous- Removable Discontinuous Infinite Discontinuous- Jump

  8. Homework • Wkst. • Bring calculators Monday

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