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2.7 Piecewise Functions

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2.7 Piecewise Functions

  1. 1. 2.7 Piecewise Functions
  2. 2. What is a Piecewise Function?• A function that combines pieces of different equations.• Each piece is for a different domain (set of x values).• Example:
  3. 3. Why Are They Important?• In real life, lots of problems are modeled by piecewise functions.• Examples: ▫ Finding shipping costs ▫ Income taxes ▫ Ordering t-shirts
  4. 4. Examples:
  5. 5. Writing Piecewise Functions• We know how to graph, now go backwards!• First, find the domains (where the graph is cut)• Then, find the slopes and y-intercepts.• Fill in the equation for each domain.• Example: ___ x + ___ , if x ______ ___ x + ___ , if x ______
  6. 6. Example: ___ x + ___ , if x ______ ___ x + ___ , if x ______
  7. 7. Your Turn! ___ x + ___ , if x ______ ___ x + ___ , if x ______
  8. 8. Evaluating from a Graph• Move left/right to the x you need, then move up/down to find y.• Example:• Evaluate f(x) for the function shown when:• x = -3• x = -1•x=2
  9. 9. Your Turn!• Evaluate f(x) for the function shown when:•x = -1•x = 1•x = 2•x = 4
  10. 10. Evaluating Piecewise Functions• The domain tells you which equation to use.• Evaluate f(x) when:a)x = 0b)x = 2c)x = 4
  11. 11. Your Turn!• Evaluate f(x) when:•x = 0•x = 3•x = 6
  12. 12. Step FunctionsEach piece of the function is a flat,horizontal line.

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