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# 2.3.1 properties of functions

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### 2.3.1 properties of functions

1. 1. 2.3 Properties of Functions<br />Even, Odd, or Neither (Symmetry)<br />Increasing and Decreasing Intervals<br />Local Maxima and Minima<br />
2. 2. Even Function<br />A function that is symmetric about the y-axis.<br />Algebraically – <br />
3. 3. Odd Function<br />A function that is symmetric about the origin<br /> (180⁰ rotational symmetry about the origin)<br />Algebraically - <br />same<br />
4. 4. Increasing<br />As the x-values increase, the y-values also increase<br />Describe the <br />x-values in <br />interval notation<br />
5. 5. Decreasing<br />As the x-values increase, the y-values decrease<br />Describe the <br />x-values in <br />interval notation<br />
6. 6. Constant<br />As the x-values increase, the y-value remain the same.<br />Describe the <br />x-values in <br />interval notation<br />
7. 7. Find the intercepts<br />
8. 8. State the Domain and Range<br />
9. 9. Identify the intervals where it is increasing<br />Describe the <br />x-values in <br />interval notation<br />
10. 10. Identify the intervals where it is decreasing<br />Describe the <br />x-values in <br />interval notation<br />
11. 11. Identify the intervals where it is constant<br />None<br />
12. 12. Determine whether it is even, odd, or neither<br />Symmetric about the origin – <br />Odd Function<br />
13. 13. Local Maxima and Minima<br />Local Maximum – The largest value of y on an open interval of x.<br />Local Minima – The smallest value of y on an open interval of x.<br />
14. 14. Identify the local maximum<br />The local maximum is 1, <br />and it occurs when x = π/2<br />
15. 15. Identify the local minimum<br />The local minimum is -1, <br />and it occurs when x = -π/2<br />
16. 16. Identify the local extrema on the given interval (*using a calculator)<br />
17. 17. Find Maximum<br />Estimate an <br />interval of x<br />2nd<br />TRACE (calc)<br />4:maximum<br />(-2,0)<br />
18. 18. Find Maximum<br />2nd<br />TRACE (calc)<br />4:maximum<br />(-2,0)<br />
19. 19. Find Maximum<br />-2 ENTER<br />0 ENTER<br />ENTER<br />(-2,0)<br />Maximum is 11.53, occurs at x= -.82<br />
20. 20. Find Minimum<br />Estimate an <br />interval of x<br />2nd<br />TRACE (calc)<br />3:minimum<br />(0,2)<br />
21. 21. Find Minimum<br />0 ENTER<br />2 ENTER<br />ENTER<br />(0,2)<br />Minimum is -1.53, occurs at x= .82<br />
22. 22. Assignment<br />p. 88 <br /># 7, 10 - 28 even,<br />39 - 46, 63, 65, 66<br />