warmup 5 How do you think you did

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warm_up #5 • How do you think you did on the last test? •

warm_up #5 • How do you think you did on the last test? • What parts did you do well in? • What parts could you have improved upon? 12/4/2020 1 -9 Parent Functions 1

Grade Distribution A B C D F No Show Avg 1 st 7 16

Grade Distribution A B C D F No Show Avg 1 st 7 16 4 3 0 1 83. 64 3 rd 4 12 6 2 5 2 77. 89 7 th 6 13 4 4 3 1 80. 31

Introduction to Parent Functions Section 1 -9 12/4/2020 1 -9 Parent Functions 3

Introduction to Parent Functions Section 1 -9 12/4/2020 1 -9 Parent Functions 3

What is a parent function? • The parent function is the simplest function with

What is a parent function? • The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function. 12/4/2020 1 -9 Parent Functions 4

Parent Functions Family Constant Linear Quadratic Cubic Rule f(x) = c f(x) = x

Parent Functions Family Constant Linear Quadratic Cubic Rule f(x) = c f(x) = x 2 f(x) = x 3 Domain (–∞, ∞) Range C (–∞, ∞) [0, ∞) (–∞, ∞) Zeros None (0, 0) Symmetry y-axis Origin Graph 12/4/2020 1 -9 Parent Functions 5

Parent Functions Family Squ Root Abs Value Reciprocal Rule f(x) = √x f(x) =

Parent Functions Family Squ Root Abs Value Reciprocal Rule f(x) = √x f(x) = |x| f(x) = Domain [0, ∞) (–∞, 0) U (0, ∞) Range [0, ∞) (–∞, 0) U (0, ∞) Zeros (0, 0) None Symmetry None y-axis Origin Graph 12/4/2020 1 -9 Parent Functions 6

Get some exercise 12/4/2020 1 -9 Parent Functions 7

Get some exercise 12/4/2020 1 -9 Parent Functions 7

Example 1 Identify the parent function for g from its function rule. Graph g(x)

Example 1 Identify the parent function for g from its function rule. Graph g(x) on your calculator and describe what transformation of the parent function it represents. Then, identify the domain and range of the transformation. Linear Function, Down 3 Domain: (–∞, ∞) Range: (–∞, ∞) 12/4/2020 1 -9 Parent Functions 8

Example 2 Identify the parent function for g from its function rule. Graph g(x)

Example 2 Identify the parent function for g from its function rule. Graph g(x) on your calculator and describe what transformation of the parent function it represents. Then, identify the domain and range of the transformation. Quadratic Function, Shrinks with scale of 2 OR Horizontal Compression of 1/2 Domain: (–∞, ∞) Range: [0, ∞) 12/4/2020 1 -9 Parent Functions 9

Example 3 Identify the parent function for g from its function rule. Graph g(x)

Example 3 Identify the parent function for g from its function rule. Graph g(x) on your calculator and describe what transformation of the parent function it represents. Then, identify the domain and range of the transformation. Quadratic Function, Reflection Domain: (–∞, ∞) Range: (–∞, 0] 12/4/2020 1 -9 Parent Functions 10

Your Turn Identify the parent function for g from its function rule. Graph g(x)

Your Turn Identify the parent function for g from its function rule. Graph g(x) on your calculator and describe what transformation of the parent function it represents. Then, identify the domain and range of the transformation. Cubic Function, Moves 2 units to the Right, Grows by a scale of 1/(Hor. Stretch by 2 ) Domain: (–∞, ∞) Range: (–∞, ∞) 12/4/2020 1 -9 Parent Functions 11

Example 4 Identify the parent function for g from its function rule. Graph g(x)

Example 4 Identify the parent function for g from its function rule. Graph g(x) on your calculator and describe what transformation of the parent function it represents. Then, identify the domain and range of the transformation. Square Root Function, Reflection on x-axis, Vertical Stretch Domain: [0, ∞) Range: (–∞, 0] 12/4/2020 1 -9 Parent Functions 12

Example 5 Determine from the data from this set of ordered pairs, describe the

Example 5 Determine from the data from this set of ordered pairs, describe the parent function, and the transformation that best approximates the data set. x – 2 – 1 0 1 2 12/4/2020 y 2 – 1 – 2 – 1 2 Determine the equation and the slope A) Graph it B) If the ‘y’ difference and if ‘x’ are consistent: …differs 1 time: LINEAR …differs 2 times: QUADRATIC …differs 3 times: CUBIC More then two times, it can be EXPONENTIAL, CUBIC, or SQUARE ROOT 1 -9 Parent Functions 13

Example 5 Determine from the data from this set of ordered pairs, describe the

Example 5 Determine from the data from this set of ordered pairs, describe the parent function, and the transformation that best approximates the data set. x – 2 – 1 0 1 2 12/4/2020 y 2 – 1 – 2 – 1 2 Linear Quadratic Shift of Vertical down shift of 2 1 -9 Parent Functions 14

Example 6 Determine from the data from this set of ordered pairs, describe the

Example 6 Determine from the data from this set of ordered pairs, describe the parent function, and the transformation that best approximates the data set. x – 2 – 1 0 1 2 12/4/2020 y – 6 1 2 3 10 Cubic, Vertical Shift of 2 1 -9 Parent Functions 15

Your Turn Determine from the data from this set of ordered pairs, describe the

Your Turn Determine from the data from this set of ordered pairs, describe the parent function, and the transformation that best approximates the data set. x 0 1 2 3 4 12/4/2020 y 0 1 1. 414 1. 732 2 Square Root, No Shift 1 -9 Parent Functions 16

Assignment Pg 71 3 -27 odd, 39 A-D Know the Parent Function Chart 12/4/2020

Assignment Pg 71 3 -27 odd, 39 A-D Know the Parent Function Chart 12/4/2020 1 -9 Parent Functions 17