Example 1: Consumer Application Warm Up Write the equation of each line in slope-intercept form. 1. Slope of 3 and passes through the point (50, 200) 9-2 LEARNING GOALS 9.2.1 Write and graph piecewise functions. 9.2.2 Use piecewise functions to describe real-world situations. A piecewise function is a function that is a combination of one or more functions. It has different _________ for different parts of the ___________. A step function is Example 1: Consumer Application A. Create a table & verbal description to represent the graph. Step 1 Create a table Step 2 Write a verbal description.

Example 2: Evaluating a Piecewise Function B. Create a table & verbal description to represent the graph. Step 1 Create a table Step 2 Write a verbal description. Green Fee ($) Time Range (h) To __________________ any piecewise function for a specific __-value, find the ____________ listed that contains that ___-value and plug in your ___-value for the corresponding rule. Example 2: Evaluating a Piecewise Function A. Evaluate each piecewise function for x = –1 and x = 4. 2x + 1 if x ≤ 2 x2 – 4 if x > 2 h(x) = B. Evaluate each piecewise function for x = –1 and x = 3. 12 if x < –3 20 if x ≥ 6 f(x) = 15 if –3 ≤ x < 6

Example 3: Graphing Piecewise Functions You graph a piecewise function by graphing each piece of the function. Example 3: Graphing Piecewise Functions A. Graph each function. g(x) = ¼x + 3 if x < 0 –2x + 3 if x ≥ 0 x -4 -2 2 4 B. Graph each function. x2 – 3 if x < 0 g(x) = ½x – 3 if 0 ≤ x < 4 (x – 4)2 – 1 if x ≥ 4 x -4 -2 1 2 3 4 6 8

C. Graph the function. 4 if x ≤ –1 f(x) = –2 if x > –1 D. Graph the function. –3x if x < 2 g(x) = x + 3 if x ≥ 2

Example 4: Application A. Shelly earns $8 an hour for the first 40 hours she works. She earns $12 an hour for each hour over 40 that she works. Sketch a graph of Shelly’s earnings versus the number of hours that she works up to 60 hours. Then write a piecewise function for the graph. Step 1 Make a table to organize the data. Step 2 Because the number of hours worked is the independent variable, determine the intervals for the function. Shelly’s Earnings Hours worked Pay ($/hr) Step 3 Write a linear function for each leg. f(h) = Step 4 Graph the function.

B. Jennifer is completing a 15. 5-mile triathlon. She swims 0 B. Jennifer is completing a 15.5-mile triathlon. She swims 0.5 mile in a ½ hour, bicycles 12 miles in 1 hour, and runs 3 miles in a ½ hour. Sketch a graph of Jennifer’s distance versus time. Then write a piecewise function for the graph. Step 1 Make a table to organize the data. Use the distance formula to find Jennifer’s rate (speed) for each leg of the race and determine the intervals for time in each leg of the race. Recall r = d/t Activity Time Interval Speed Swimming Running Biking Step 3 Graph the function. Step 4 Write a function for each leg. d(t) =