2. CHAPTER 2 LESSON 6 Special Functions

3. Vocabulary Step Function- A function whose graph is a series of line segments Greatest Integer Function- A step function, written as f(x)= [[ x ]], where f(x) is the greatest integer less than or equal to x Constant Function- A function, written as f(x)=b, where m=0 so f(x)=b for all x values Identity Function- A function, written as f(x)=x, where m=1 so y=x for all x values Absolute Value Function- A function, written as f(x)= ∣x∣, where f(x)= the positive form of x Piecewise Function- A function that is written using two or more expressions

4. Greatest Integer What is the greatest integer less than or equal to the following numbers?

5. Greatest Integer Function

6. Domain is all real numbers Range is only integers, or Z

7. Step Function

8. Domain is all real numbers Range depends on equation

9. Changes that can be made to step functions If adding a number (inside or outside) to the step function, the graph moves up. If subtracting a number (inside or outside) to the step function, the graph moves down.

10. Examples

11. Changes that can be made to step functions If multiplying a number inside the step function, the length of the steps is smaller, but the distance between the steps stays the same. If multiplying a number outside the step function, the length of the steps is the same, but the distance between the steps is increased.

12. Examples

13. Changes that can be made to step functions If dividing by a number inside the step function, the length of the step is larger, but the distance between the steps stays the same. If dividing by a number outside the step function, the length of the step is the same, but the distance between the steps is smaller.

14. Examples

16. Changes that can be made to step functions If multiplying or dividing by a negative number, the steps go downward instead of upwards, but the rules for step length and distance between steps still apply

17. Examples

18. Constant Function

19. Domain is all real numbers Range is b from f(x)=b

20. Examples

21. Identity Function

22. Identity Function y=x Domain is all real numbers Range is all real numbers

23. Absolute Value Function

24. Domain is all real numbers Range depends on equation

25. Changes that can be made to Absolute Value functions If adding a number inside the absolute value, the graph moves to the left. If adding a number outside the absolute value, the graph moves up.

26. Examples

29. Changes that can be made to Absolute Value functions If subtracting a number inside the absolute value, the graph moves to the right. If subtracting a number outside the absolute value, the graph moves down.

30. Examples

32. Changes that can be made to Absolute Value functions If multiplying by a number (inside or outside) to the absolute value, the graph is skinnier. If dividing by a number (inside or outside) to the absolute value, the graph is wider.

33. Example

35. Changes that can be made to Absolute Value functions If multiplying or dividing by a positive number, the absolute value looks like V. If multiplying or dividing by a negative number, the absolute value looks like Λ.

36. Example

38. Piecewise Function

39. Domain and Range vary depending on the different pieces

40. Examples

43. Homework Worksheet 2-6