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**3-8 transforming polynomial functions**

Chapter 3 3-8 transforming polynomial functions

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SAT Problem of the day Lines l and m are perpendicular lines that intersect at the origin. If line l passes through the point (2,-1), then line m must pass through which of the following points? A) (0,2) B)(1,3) C)(2,1) D)(3,6) E)(4,0)

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solution Right Answer: D

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Objectives Transform polynomial functions.

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**Transforming polynomial functions**

You can perform the same transformations on polynomial functions that you performed on quadratic and linear functions.

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**Transforming Polynomial functions**

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Example#1 Translating polynomial For f(x) = x3 – 6, write the rule for each function and sketch its graph. g(x) = f(x) – 2 Solution: To graph g(x) = f(x) – 2, translate the graph of f(x) 2 units down. This is a vertical translation.

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Example#1 continue

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Example#2 For f(x) = x3 – 6, write the rule for each function and sketch its graph. h(x) = f(x + 3) Solution: To graph h(x) = f(x + 3), translate the graph 3 units to the left. This is a horizontal translation.

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Example#2 continue

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Example#3 For f(x) = x3 + 4, write the rule for each function and sketch its graph. g(x) = f(x) – 5 Solution: To graph g(x) = f(x) – 5, translate the graph of f(x) 5 units down. This is a vertical translation.

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Example#3 continue

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**Student guided practice**

Do problems 1 and 4 in your book page 207

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**Reflecting polynomial functions Example#4**

Let f(x) = x3 + 5x2 – 8x + 1. Write a function g that performs each transformation. Reflect f(x) across the x-axis. Solution : g(x) = –f(x) g(x) = –(x3 + 5x2 – 8x + 1) g(x) = –x3 – 5x2 + 8x – 1

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Example#5 Let f(x) = x3 + 5x2 – 8x + 1. Write a function g that performs each transformation. Reflect f(x) across the y-axis. Solution: g(x) = f(–x) g(x) = (–x)3 + 5(–x)2 – 8(–x) + 1 g(x) = –x3 + 5x2 + 8x + 1

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**Student guided practice**

Do problems 5 and 6 in your book page 207

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**Do compressions/stretches**

Let f(x) = 2x4 – 6x Graph f and g on the same coordinate plane. Describe g as a transformation of f. Solution: g(x) = 1/2f(x) g(x) = 1/2 (2x4 – 6x2 + 1) g(x) = x4 – 3x2 + 1/2 g(x) is a vertical compression of f(x).

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Example continue

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Example Let f(x) = 2x4 – 6x Graph f and g on the same coordinate plane. Describe g as a transformation of f. g(x) = f( 1/3 x) Solution: g(x) = 2( 1/3x)4 – 6(1/3x)2 + 1 g(x) = 2/81x4 – 2/3 x2 + 1 g(x) is a horizontal stretch of f(x).

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**Student guided practice**

Do problems 7-9

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**Combining transformations**

Write a function that transforms f(x) = 6x3 – 3 in each of the following ways. Support your solution by using a graphing calculator. Compress vertically by a factor of 1/3 , and shift 2 units right. Solution: g(x) = 1/3f(x – 2) g(x) = 1/3(6(x – 2)3 – 3) g(x) = 2(x – 2)3 – 1

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**Reflect across the y-axis and shift 2 units down.**

Write a function that transforms f(x) = 6x3 – 3 in each of the following ways. Support your solution by using a graphing calculator. Reflect across the y-axis and shift 2 units down. Solution: g(x) = f(–x) – 2 g(x) = (6(–x)3 – 3) – 2 g(x) = –6x3 – 5

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**Student guided practice**

Do problems pg. 207

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Homework!! Do problems page 207 and 208 in your book

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**Closure Today we learn about transforming polynomial**

Next class we are going to learn about Exponential functions , growth, and decay

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