3. 2-6 Special Functions Objectives Students will be able to: 1) identify and graph step, constant, and identity functions 2) Identify and graph absolute value and piecewise functions

4. I. Constant Functions A constant function is a function whose (output) value is the same for every input value.

5. II. Linear Functions Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable.

6. III. Identity Function The identity function always returns the same value that was used as its argument. The function is given by f(x) = x. * Most basic form of Linear Function

7. IV. Absolute Value Functions

10. When a constant is added on the outside of the absolute value symbol and is…. – Positive: the graph moves up – Negative: the graph moves down When a constant is added on the inside of the absolute value symbol and is… – Positive: the graph moves to the left – Negative: the graph moves to the right

11. Domain: Range:

12. V. Piecewise Functions A piecewise function is a function that is written using two or more expressions. The function is broken up into multiple pieces on a graph.

16. The cost of the postage to mail a letter is a function of the weight of the letter. But the function is not linear. It is a special function called a step function. The graph of a step function consists of line segments or rays.

17. VI. Greatest Integer Function

18. Graph each step function. Identify the domain and range. a) Domain: Range:

19. b) Domain: Range:

20. c) Domain: Range:

21. Summary