7­7 Day 1 Inverse Relations and Functions March 03, 2009
7­7 Inverse Relations and Functions
Day 1
Objective: Find the inverse of a relation or function.
Feb 28­12:54 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Graph each pair of functions on a single coordinate plane.
Feb 28­12:56 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Activity: Inverses
Open your book to page 406 and
complete numbers 1 and 2 (ONLY)
from the activity in your notes.
Mar 1­10:31 AM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Mar 1­10:31 AM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Mar 1­10:31 AM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Mar 1­10:31 AM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
The Inverse of a Function
If a relation pairs element a of its domain to element b of its range, the inverse relation pairs b with a. relation
(a, b)
inverse
(b, a)
The domain and range are reversed from the relation to the inverse.
Example: Relation r
Domain Range
1.2
1
1.4
1.6
2
1.9
Inverse of r
Domain Range
1.2
1
1.4
1.6
2
1.9
Feb 28­12:57 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Example #1: Finding the Inverse of a Relation
a. Find the inverse of relation s.
Relation s
Inverse of Relation s
x 1 2 3 4
y ­1 0 1 1
x
y
Feb 28­12:58 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Example #1: Finding the Inverse of a Relation
Relation s
Inverse of Relation s
x 1 2 3 4
y ­1 0 1 1
x ­1 0 1 1
y 1 2 3 4
b. Graph s and its inverse.
Relation s
Inverse of s Feb 28­12:59 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Example #1: Finding the Inverse of a Relation
c. Describe how the line y = x is related to the graphs of s and its inverse.
d. Is relation s a function? Is the inverse of s a function?
Relation s
Inverse of s
Feb 28­12:59 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
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Feb 28­12:59 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Example #2: Interchanging x and y.
a. Find the inverse of y = x2 + 3.
y = x2 + 3
x = y2 + 3
x ­ 3 = y2
y = ±√x ­ 3
b. Is y = x2 + 3 a function? Is the inverse a function? Explain. Feb 28­12:59 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Example #2: Interchanging x and y.
c. Graph y = x2 + 3 and its inverse, y = ±√x ­ 3
Feb 28­12:59 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Example #3: Interchanging x and y.
a. Find the inverse of y = 3x ­ 10.
b. Is the inverse a function? Explain. Feb 28­12:59 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Example #3: Interchanging x and y.
c. Graph y = 3x ­ 10 and its inverse.
Feb 28­12:59 PM
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7­7 Day 1 Inverse Relations and Functions March 03, 2009
Homework:
page 410 (1 ­ 20)
Mar 1­11:14 AM
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