1. 2. Warm-Up Domain Range INQ:______________ INT:______________ Is it a function?_______ Is it discrete, continuous? 2. Domain Range INQ:______________ INT:______________ Is it a function?_______ Is it discrete, continuous?

Unit 3 PIECEWISE FUNCTIONS

Objectives I can evaluate piecewise functions. I can graph piecewise functions.

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

The rule for a piecewise function is different for different parts, or pieces, of the domain. For instance, movie tickets prices are often different for different ages groups. So the function for movie ticket prices would assign a different value (ticket price) for Each domain interval (age group). Remember: When using interval notation, square brackets [ ] indicate an included endpoint, and parentheses ( ) indicate an excluded endpoint

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

Piecewise Function – A function defined in pieces.

 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 -

REAL WORLD The graph shows the monthly fee for Cell Zone. Use it to answer the following questions: 1) What is the monthly fee? 2) How many minutes are included in the monthly fee? 3) If a customer goes over the minutes included in the fee, how much will they be charged per minute ($/min)? 4) Write a function for this plan.

1. Graph the function, and evaluate at x = 1 and x = 3. Lesson Quiz: Part I 1. Graph the function, and evaluate at x = 1 and x = 3. x2 + 2 if x ≤ 2 1 2 p(x) = x + 3 if x > 2 1 2

Lesson Quiz: Part II 2. Write and graph a piecewise function for the following situation. A house painter charges $12 per hour for the first 40 hours he works, time and a half for the 10 hours after that, and double time for all hours after that. How much does he earn for a 70-hour week?

RECALL

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

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

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

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

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