Key Features of a Graph. Warm Up What do you think the key features are of a graph? Write them down.

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1 Warm Up What do you think the key features are of a graph? Write them down. 1

2 Domain and Range x intercepts and y intercepts Intervals of increasing, decreasing, and constant behavior Parent Equations Maxima and Minima 2

3 We already know that domain is the set of all x values (input values), and we know how to find this algebraically (like we did in class yesterday). Now we are going to find the domain by looking at the graph of a function. 3

4 Don't forget your Including/Excluding Symbols! Including Excluding 4

5 Steps for Finding Domain Start at the far left of the graph. (Just like we read...left to right) Move along the x axis until you find the lowest possible x value of the graph. This is your lower bound. Note if you have a open circle or a closed circle. Keep moving along the x axis until you find your highest possible x value of the graph. This is your upper bound. Note if you have a open circle or a closed circle. 5

6 Domain: 6

7 Domain: 7

8 Domain: 8

9 Warm Up: Find the domain, and explain how you found it. Domain: 9

10 Domain: Domain: 10

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12 Range The set of all possible output or y values To find the range of the graph we look at the y axis of the graph We also use open and closed circles for the range 12

13 Steps for finding the Range of a Function: Start at the bottom of the graph. Move along the y axis until you find the lowest possible y value of the graph. This is your lower bound. Note if you have a open circle or a closed circle. Keep moving along the y axis until you find your highest possible y value of the graph. This is your upper bound. Note if you have a open circle or a closed circle. 13

14 Range: 14

15 Range: 15

16 Alternative way of finding Range: Rotate and find domain. 16

17 Alternative way of finding Range: Rotate and find domain. 17

18 Range: Range: 18

19 Challenge: Find the domain & RANGE of each. 19

20 X Intercepts: Where the function crosses the x axis. Has many names: Roots Zeros X Intercepts 20

21 What are the x intercepts of this function? 21

22 What are the x intercepts of this function? 22

23 What are the y intercepts of this function? What is a y intercept? 23

24 Warm Up: What are the intercepts of this function? 24

25 Types of Function Behavior: There are 3 Types of Function Behavior: Increasing Decreasing Constant Just like the other things we have done in class you always read this from LEFT TO RIGHT!!! 25

26 As x is increasing (as we go from left to right)...y is also increasing. 26

27 As x increases, y stays the same (AKA???). 27

28 As x increases, y is decreasing. This is known as an inverse relationship. 28

29 Identifying Intervals of Behavior Process: We are going to use interval notation just like we did for finding the Domain & Range. The interval measures the x values. The description of the behavior gives the y values. 29

30 Identifying Intervals of Behavior Process: We are going to use interval notation just like we did for finding the Domain & Range. The interval measures the x values. The description of the behavior gives the y values. The y values are increasing. Increasing: [0,4) The x values are between 0 and 4 including 0, but not including 4. 30

31 Identify the intervals for which the function is: Increasing Decreasing Constant 31

32 Identify the intervals for which the function is: Increasing Decreasing Constant 32

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39 What do you think of when you hear the word parent? 39

40 Types of Parent Functions Linear Quadratic Cubic Square Root Cubed Root Reciprocal Absolute Value 40

41 Linear y=x 41

42 Quadratic y=x 2 42

43 Cubic y=x 3 43

44 Square Root y= x 44

45 Cubed Root y= x 45

46 Reciprocal y=1/x 46

47 Absolute Value y= 47

48 "Baby Functions" Look and behave similarly to their parent functions. To get a baby functions, add, subtract, multiply, and/or divide parent equations by (generally) constants f(x) = x 2 f(x) = 5x 2 14 f(x) = 1/x f(x) = 4 (2/x) f(x) = x 3 f(x) = 2x 3 + 4x 2 x

49 To identify what a function's "Parent" is: Look for obvious symbols such as square root signs, cubed root signs, absolute value signs, and fractions with an x in the denominator. If there are no crazy symbols then look for the highest exponent that there is in the problem. (the degree tells you what type of function it is if there are no other crazies involved). 49

50 Identify the parent functions. f(x) = 1 x+2 50

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53 Identify the parent functions. Peaks or hills are maximum points. Valleys are your minimum points. 53

54 Identify the maximum and minimum points. Maximum: Minimum: Write answers in ordered pairs. 54

55 Identify the maximum and minimum points. Maximum: Minimum: Write answers in ordered pairs. 55

56 Identify the maximum and minimum points. Maximum: Minimum: Write answers in ordered pairs. 56

57 Identify the parent functions. f(x) = 1 x+2 57

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