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Section 2.3 Piecewise Defined Functions 2

Piecewise Defined Functions- when a function uses different formulas on different parts of its domain. 3Page 73

Piecewise Defined Functions- when a function uses different formulas on different parts of its domain. An example: 4Page 73

Here is a graph of this piecewise function: 5Page 73

Piecewise Defined Functions- Another example: g(x) = x + 1 for x ≤ 2 and g(x) = 1 for x > 2 Let's graph this function: 6Page 73 Example 1

g(x) = x + 1 for x ≤ 2 and g(x) = 1 for x > 2 7Page 73

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. a. Use bracket notation to write a formula for the cost, C, of a call as a function of its length t in minutes. b. Graph the function. c. State the domain and range of the function. 8Page 2 Example #2

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. a. Use bracket notation to write a formula for the cost, C, of a call as a function of its length t in minutes. 9Page 74

You can simplify this expression to get: 10Page 74

But you lose the real meaning by doing so. 11Page 74

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. b. Graph the function. 12Page 74

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. b. Graph the function. 13Page 74

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function. 14Page 74

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function. Domain: t > 0 (call lengths ≤ 0 are silly) 15Page 74

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function. Domain: t > 0 (call lengths ≤ 0 are silly) Range? 16Page 74

A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. Range? We can see that the range is: C ≥ 99 17Page 74

The Absolute Value Function 18Page 76

The Absolute Value Function (defined piecewise): 19Page 76

Some examples: 20Page 76

Some examples: 21Page 76

Some examples: 22Page 76

Some examples: 23Page 76

Let's form a table and then graph the absolute value function: 24Page 76

x|x||x| −33 −22 − Page 76

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This completes Section Page