Chapter 3
-
Upload
thane-whitney -
Category
Documents
-
view
23 -
download
0
description
Transcript of Chapter 3
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)
Transforming polynomial functions You can perform the same transformations
on polynomial functions that you performed on quadratic and linear functions.
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.
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.
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.
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
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
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).
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).
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
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