2-2 Extension Part 2: Piecewise Functions

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

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

f(x) = Evaluating Piecewise Functions: Evaluating piecewise functions is just like evaluating functions that you are already familiar with. Let’s calculate f(2). f(x) = x2 + 1 , x  0 x – 1 , x  0 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

f(x) = Let’s calculate f(-2). x2 + 1 , x  0 x – 1 , x  0 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

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

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

 f(x) = Graphing Piecewise Functions: x2 + 1 , x  0 x – 1 , x  0 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. 

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

Graphing Piecewise Functions Domain - Range -

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

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

 

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

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

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