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Piecewise-Defined Functions

Piecewise-Defined Functions. Lesson 2.5. Piecewise Defined Functions. Consider a function defined differently for different parts of the domain (the x values) Consider what the table of values looks like. Piecewise Defined Functions. Use Diamond 0 for the ≤ sign.

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Piecewise-Defined Functions

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  1. Piecewise-Defined Functions Lesson 2.5

  2. Piecewise Defined Functions • Consider a function defined differently for different parts of the domain (the x values) • Consider what the table of values looks like

  3. Piecewise Defined Functions

  4. Use Diamond 0 for the ≤ sign Piecewise Defined Functions • Our calculatorhandles piecewisefunctions with thewhen ( ) command What will the graph look like?

  5. Piecewise Defined Functions

  6. Piecewise Defined Functions • Condition • Expression to usewhen conditionis true • Expression to use when condition is false

  7. Piecewise Defined Functions • Try entering and graphing the following function

  8. Piecewise Defined Functions

  9. Absolute Value Function • Whatever you put into the functioncomes out positive -3 +7 +7 +3

  10. Absolute Value Function • Definition Use the abs( ) function on your calculator

  11. Absolute Value Function • Note the graph of y = | x | • Table of values

  12. Absolute Value Inequalities • |a x + b | < k is equivalent to • - k < a x + b < k • - k < a x + b and a x + b < k 7

  13. ) ) Absolute Value Inequalities • |a x + b | > k is equivalent to • a x + b < -k or a x + b > k 7

  14. Try It Out! • |15 – x | < 7 • Solve symbolically • |5x – 7 | > 2 • Show graphical solution

  15. Assignment • Lesson 2.5 • Page 133 • Exercises 1 – 77 EOO

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