1. 1 Section 1.3; Page 99

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4. 4 Domain and Range has no meaning when x is negative  x = [-2:0.1:2] y = sqrt(4 - x.^2) plot (x,y) Only valid for x between -2 and +2 inclusive Set of numbers for which the function is defined is called the domain of the function. Range, the values of y (function) can take has no meaning when x is 0  Domain is input range is output This is similar to example 6

5. 5 Numerator: x ≥ 0 Denominator should be both positive and greater than 0 We need to satisfy the conditions for the numerator and the denominator  0 ≤ x < 2 For tow products to be positive, they both must be positive Numerator: -2≤ x ≤ 2 Denominator: x > 0 function: 0 < x ≤ 2

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21. 21 Section 1.5Shifting, Reflecting, and Stretching Graphs Summary of Graphs of Common Functions

22. 22 Vertical and Horizontal Shifts (p126) Note: shift to the right

23. 23 -  DOWN -  RIGHT

24. 24 +  SHIFT LEFT + 1  SHIFT UP

25. 25 SHIFT LEFT  + SHIFT DOWN  -

26. 26 Reflecting Graphs

27. 27 MULTIPLY THE WHOLE BY - SUBSTITUTE -x for x

28. 28 Flip and add 2 Flip and add move right by 3  -3 Page 128

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30. 30 Nonrigid Transformations a change in the shape of the original graph

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33. 33 1.6 Combinations of Functions Just simply write it separately

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35. 35 Try this please

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37. 37 Ignore this and look at the same example we did last class – on slide 5

38. 38 Compositions of Functions Pay attention to new symbol

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42. 42 Now to be fancy, refer to n as a function h(x), and m as a function f(x)