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Chapter 3

Chapter 3. 3-8 transforming polynomial functions. 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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Chapter 3

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  1. Chapter 3 3-8 transforming polynomial functions

  2. 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)

  3. solution • Right Answer: D

  4. Objectives • Transform polynomial functions.

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

  6. Transforming Polynomial functions

  7. 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.

  8. Example#1 continue

  9. 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.

  10. Example#2 continue

  11. 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.

  12. Example#3 continue

  13. Student guided practice • Do problems 1 and 4 in your book page 207

  14. 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

  15. 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

  16. Student guided practice Do problems 5 and 6 in your book page 207

  17. Do compressions/stretches • Let f(x) = 2x4 – 6x2 + 1. 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).

  18. Example continue

  19. Example • Let f(x) = 2x4 – 6x2 + 1. 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).

  20. Student guided practice • Do problems 7-9

  21. 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

  22. 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

  23. Student guided practice • Do problems 10-12 pg. 207

  24. Homework!! • Do problems 14-20 page 207 and 208 in your book

  25. Closure • Today we learn about transforming polynomial • Next class we are going to learn about Exponential functions , growth, and decay

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