WHAT IS A FUNCTION? WHAT IS THE DOMAIN OF A FUNCTION? THE RANGE? WHAT DOES A PIECEWISE GRAPH LOOK LIKE? HOW DO YOU WRITE A PIECEWISE FUNCTION? Piecewise Functions (2.7)

Warm Up #1. Evaluate f(x)=3x-2 when x = -2. #2. Graph the lines –x+y=-2 and y = 1/3x – 2 on the same coordinate grid.

Piecewise Functions Combination of equations Each “piece” of the function corresponds to a part of the domain EXAMPLE: 3x +2 is the function only when x < 3. x-1 is the function only when x > 3

Evaluating Need to evaluate the function using the piece that contains the value of x in its domain: Evaluate : a.) g(0)b.)g(10)c.) g(3)d.)g(-2)

Graphing a Piecewise Function Pay attention to where the function changes The graph may or may not be connected where it changes “pieces” Example: Graph

Examples: Graph the following. 1.2.

Step Function Graph resembles steps

Step Functions Write a function for the graph below:

Writing a Piecewise Function Write the equation for each piece of the function from the graph Pay attention to the domain (where does the piece of the graph cover the x-axis?) Be aware of solid vs. open circles

Example Shipping costs $6 on purchases up to $50, $8 on purchases over $50 up to $100, and $10 on purchases over $100 up to $200. Write a piecewise function for these charges. Give the domain and range.

Example A plane descends from 5000 ft at 250 ft/min for 6 min. Over the next 8 min, it descends at 150 ft/min. Write a piecewise function for the altitude A in terms of the time t. What is the plane’s altitude after 12 min?