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2-2 Extension Part 2: Piecewise Functions

Learn how to evaluate and graph piecewise functions defined by multiple functions over specified domains. Practice calculating values such as f(2) and graphing shapes like parabolas and lines. Explore various examples with clear explanations.

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2-2 Extension Part 2: Piecewise Functions

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  1. 2-2 Extension Part 2:Piecewise Functions

  2. Definition: Piecewise Function –a function defined by two or more functions over a specified domain.

  3. What do they look like? x2 + 1 , x  0 x – 1 , x  0 f(x) = You can EVALUATE piecewise functions. You can GRAPH piecewise functions.

  4. Evaluating Piecewise Functions: Evaluating piecewise functions is just like evaluating functions that you are already familiar with. x2 + 1 , x  0 x – 1 , x  0 f(x) = Let’s calculate f(2). You are being asked to find y when x = 2. Since 2 is  0, you will only substitute into the second part of the function. f(2) = 2 – 1 = 1

  5. Let’s calculate f(-2). x2 + 1 , x  0 x – 1 , x  0 f(x) = You are being asked to find y when x = -2. Since -2 is  0, you will only substitute into the first part of the function. f(-2) = (-2)2 + 1 = 5

  6. Your turn: 2x + 1, x  0 2x + 2, x  0 f(x) = Evaluate the following: f(-2) = -3 ? f(5) = 12 ? f(1) = 4 ? f(0) = ? 2

  7. One more: 3x - 2, x  -2 -x , -2  x  1 x2 – 7x, x  1 f(x) = Evaluate the following: f(-2) = 2 ? ? f(3) = -12 ? f(-4) = -14 ? f(1) = -6

  8. Graphing Piecewise Functions: x2 + 1 , x  0 x – 1 , x  0 f(x) = Determine the shapes of the graphs. Parabola and Line Determine the boundaries of each graph.   Graph the line where x is greater than or equal to zero. Graph the parabola where x is less than zero.           

  9. Graphing Piecewise Functions: 3x + 2, x  -2 -x , -2  x  1 x2 – 2, x  1 f(x) = Determine the shapes of the graphs. Line, Line, Parabola Determine the boundaries of each graph.                   

  10. Graphing Piecewise Functions Domain - Range -

  11. Domain - (-7, 7] (-4, -2), [-1, 4] Range -

  12. Domain - [-6, 7] Range - [-4, 2], (4, 7)

  13. Domain - Range - Piecewise Function – Domain and Range Domain - [-7, 7] (-6, 7) Range - [-1, 5 ) (-4.5, -1], [0, 4)

  14. Domain - Domain - Range - Range - (-7, -1), (-1, 7] (-7, 4), [5, 7) [-7, -5), (-2, 7) [-1, 5), [6, 6]

  15. Domain - Domain - Range - Range - [-1, 5] [-5, 3]

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