2.6 Day 2 September 24, 2008
2­6 Families of Functions
Day 2
Objectives:
• To analyze translations
• To analyze stretches, shrinks & reflections
Sep 20­6:55 PM
1
2.6 Day 2 September 24, 2008
Absolute Value Functions
The equation has the form:
f(x)=a|x - h|+k
The graph looks like a "V"
How do a, h, and k affect the graph?
Jun 2 ­ 8:52 AM
2
2.6 Day 2 September 24, 2008
Impacts of a, h, and k on the graph:
a impacts the size
a > 1 makes the graph more narrow
0 < a < 1 makes the graph wider
a < 0 flips the graph upsidedown
h is the horizontal movement
k is the vertical movement
Sep 20­6:16 PM
3
2.6 Day 2 September 24, 2008
Graph these absolute value functions:
1. f(x)=|x+3|-2
2. f(x)=|x-1|+3
3. f(x)=-|x+1|+2
Answers are hiding!!!
Jun 2 ­ 9:10 AM
4
2.6 Day 2 September 24, 2008
Graphing y = a|x|
Parent Function
y = |x|
y = 2|x|
1
y = |x|
2
y = 2|x| is a vertical stretch of y = 1/2|x| is a vertical shrink of y = |x| by a factor of 2. y = |x| by a factor of 1/2. Each y­value is twice the Each y­value is half the corresponding y­value of the parent corresponding y­value of the parent function.
function.
Sep 21­2:50 PM
5
2.6 Day 2 September 24, 2008
Graph these absolute value functions:
1. f(x)= -|x - 4|-2
2. f(x)=3|x+2|- 4
3. f(x)=- 1/2|x - 1|+2
Answers are hiding!!!
Jun 2 ­ 9:10 AM
6
2.6 Day 2 September 24, 2008
Write the equation of the follwing absolute value functions.
y = 1/2|x + 2| ­ 4
y = ­3|x + 3| + 4
y = |x ­ 3| + 1
Sep 21­3:05 PM
7
2.6 Day 2 September 24, 2008
ANY QUESTIONS??
Jun 2 ­ 10:05 AM
8
2.6 Day 2 September 24, 2008
Homework:
Practice 2­6 Sep 23 ­ 9:32 AM
9
Attachments
Absolute Value slider.gsp