1. 3-8 transforming polynomial functions
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 – 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).

18. Example continue

19. 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).

21. Student guided practice
Do problems 7-9

22. 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

23. 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

24. Student guided practice
Do problems pg. 207

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

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