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SECTION 14.4

CONTINUITY. SECTION 14.4. Key Terms. A. Continuous graph is where f ( x ) is at x = c if and only if there are no holes, jumps, skips or gaps in the graph B. To define a Continuous graph: f ( c ) is defined exists. Continuous Functions. Discontinuity Functions. Jump

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SECTION 14.4

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  1. 14.4 - Continuity

  2. 14.4 - Continuity

  3. 14.4 - Continuity

  4. CONTINUITY SECTION 14.4 14.4 - Continuity

  5. Key Terms A. Continuous graph is where f(x) is at x = c if and only if there are no holes, jumps, skips or gaps in the graph B. To define a Continuous graph: • f(c) is defined • exists 14.4 - Continuity

  6. Continuous Functions 14.4 - Continuity

  7. Discontinuity Functions Jump Discontinuity Removable Discontinuity Infinite Asymptote • Graphs are separated under two categories: • Removable Discontinuityis where the graph is removable if the function can be made continuous by appropriately defining f(c) such as a hole • Non-Removable Discontinuity is where • Jump Discontinuity is where the graphs are separated from a graph • Infinite Asymptote is where the function approaches towards infinity 14.4 - Continuity

  8. Example 1 Determine the points at which the function discontinuous and identify the type of discontinuity Jump Discontinuity at x = 1 Removable Discontinuity at x = 2 14.4 - Continuity

  9. Example 2 Determine the points at which the function discontinuous and identify the type of discontinuity 14.4 - Continuity

  10. Your Turn Determine the points at which the function discontinuous and identify the type of discontinuity 14.4 - Continuity

  11. Example 3 Determine the points at which the function discontinuous and identify the type of discontinuity for 14.4 - Continuity

  12. Your Turn Determine the points at which the function discontinuous and identify the type of discontinuity for 14.4 - Continuity

  13. Example 4 Determine the value of c such that the function is continuous on the entire line for 14.4 - Continuity

  14. Example 5 Determine the value of c such that the function is continuous on the entire line for 14.4 - Continuity

  15. Your Turn Determine the value of c such that the function is continuous on the entire line for 14.4 - Continuity

  16. Continuity • Since continuity is considered using limits, the properties of limits carry into continuity. • Properties of Continuity (f and g are continuous at x = c) • Sum and Difference: f + g • Product: f(g) • Quotient: f/g ; g(c) ≠0 14.4 - Continuity

  17. Example 6 Use the definition of continuity and the properties of limits to show that f(x) = sin x + x3 + 5x – 2 when x = 0. 14.4 - Continuity

  18. Example 7 Use the definition of continuity and the properties of limits to show that when x = –2. 14.4 - Continuity

  19. Your Turn Use the definition of continuity and the properties of limits to show that when x = –2. 14.4 - Continuity

  20. Assignment Worksheet 14.4 - Continuity

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