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5/2/20151-9 Parent Functions1 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?

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Grade Distribution 1st3rd7th A 746 B 161213 C 464 D 324 F 053 No Show 121 Avg 83.6477.8980.31

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5/2/20151-9 Parent Functions3 Introduction to Parent Functions Section 1-9

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5/2/20151-9 Parent Functions4 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.

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5/2/20151-9 Parent Functions5 Parent Functions (–∞, ∞) [0, ∞) (0, 0) y-axis Constant f(x) = c Family Rule Graph Domain Range (–∞, ∞) C None y-axis (–∞, ∞) (0, 0) Origin (–∞, ∞) (–∞, ∞) (0, 0) Origin LinearQuadraticCubic f(x) = xf(x) = x 2 f(x) = x 3 Zeros Symmetry

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5/2/20151-9 Parent Functions6 Parent Functions Reciprocal f(x) = Family Rule Graph Domain Range Zeros Symmetry [0, ∞) [0, ∞) (0, 0) None (–∞, ∞) [0, ∞) (0, 0) y-axis Squ RootAbs Value f(x) = √xf(x) = |x| (–∞, 0) U (0, ∞) None Origin

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5/2/20151-9 Parent Functions7 Get some exercise

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5/2/20151-9 Parent Functions8 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: (–∞, ∞)

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5/2/20151-9 Parent Functions9 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, ∞)

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5/2/20151-9 Parent Functions10 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]

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5/2/20151-9 Parent Functions11 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: (–∞, ∞)

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5/2/20151-9 Parent Functions12 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]

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5/2/20151-9 Parent Functions13 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. xy –22 –1 0–2 1–1 22 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

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5/2/20151-9 Parent Functions14 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. xy –22 –1 0–2 1–1 22 LinearQuadratic Shift of Vertical down shift of 2

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5/2/20151-9 Parent Functions15 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. xy –2–6 –11 02 13 210 Cubic, Vertical Shift of 2

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5/2/20151-9 Parent Functions16 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. xy 00 11 21.414 31.732 42 Square Root, No Shift

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5/2/20151-9 Parent Functions17 Assignment Pg 71 3-27 odd, 39A-D Know the Parent Function Chart

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Section 2.7 Parent Functions and Transformations

Section 2.7 Parent Functions and Transformations

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