2 2 Extension Part 2 Piecewise Functions Definition

2 -2 Extension Part 2: Piecewise Functions

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

What do they look like? f(x) = x 2 + 1 , x 0 x – 1 , x 0 You can EVALUATE piecewise functions. You can GRAPH piecewise functions.

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

Let’s calculate f(-2). f(x) = x 2 + 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

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

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

Graphing Piecewise Functions: x 2 + 1 , x 0 f(x) = x– 1 , x 0 Determine the shapes of the graphs. Parabola and Line Determine the boundaries of each graph. Graph the parabola line where x is greater equal where x isthan less or than to zero.

Graphing Piecewise Functions: 3 x + 2, x -2 f(x) = -x , -2 x 1 x 2 – 2, x 1 Determine the shapes of the graphs. 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 Domain - (-6, 7) Domain - [-7, 7] Range - [-1, 5 ) Range - (-4. 5, -1], [0, 4)

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

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