3. Warm Up  Sit in your usual seat. Put your new tracking sheet and homework on the corner of your desk. Answer the following questions on a separate sheet of paper (and keep this paper out throughout class):  1.Represent the shaded sections of the number lines using both INEQUALITIES and INTERVAL NOTATION. 2. When do you use brackets and when do you use parentheses in interval notation? 3. When do you use positive and negative infinity in interval notation?

4. Go over classwork and homework from Friday:

5. Today’s Objectives  SWBAT determine whether or not a relation is a function using the vertical line test.  SWBAT identify where a function is increasing, decreasing, and constant using interval notation.  SWBAT find relative and absolute extrema of functions.  SWBAT determine whether or not a function is even, odd, or neither.

6. Vertical Line Test  Vertical line test: used to determine whether or not a line is a function  Place a vertical line anywhere on the graph  If you can find a single pointwhere it crosses the line twice, then it is not a function.

7. Example: Are these two graphs functions?

8. Increasing, Decreasing, & Constant  When looking at the graph from LEFT to RIGHT, when is it going up? When is it going down? When is it going straight across?

9. Example: For the following graphs, on which intervals are they increasing, decreasing, and staying constant?

10. Extrema  Extrema = extreme  the points on the graph that are either the HIGHEST (maximum) or LOWEST (minimum)  Look for where the graph changes direction

11. Relative vs. Absolute

12. Example: Find the following extrema and classify them  Relative maximum, Relative minimum, absolute maximum, or absolute minimum?

13. Symmetry  If something is symmetrical, it is identical on either side of a line:

14. Symmetrical Functions  Even: symmetrical about the y-axis

15. Symmetrical Functions  Odd: symmetrical about origin

16. Symmetrical Functions  Neither:

17. Example: are the functions even, odd, or neither?

18. Independent Practice  Complete the practice problems.  To get your classwork stamp, you must complete at LEAST questions 1 – 5  Your homework is to finish the rest of the practice problems!

19. Exit Ticket 1. Given the following graph: a. Is it a function? How do you know? b. Using interval notation, describe where the function is decreasing. c. Identify its extrema—is it a max or min? d. Is the function even, odd, or neither?

20. Test Return  You have two weeks from today to complete a retake if you would like to.  HOWEVER -> You are only allowed 1 retake per quarter  If you choose to do a retake, you must attend a day of tutoring FIRST to fix your mistakes, and then schedule another day after school to retake the test.