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2-2 Extension Part 2: Piecewise Functions

2-2 Extension Part 2: Piecewise Functions. Definition: Piecewise Function –a function defined by two or more functions over a specifie d domain. What do they look like?. x 2 + 1 , x  0 x – 1 , x  0. f(x) =. You can EVALUATE piecewise functions.

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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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