7-7 Day 1 Inverse Relations and Functions.pdf
7-7 Day 1 Inverse Relations and Functions.pdf
7-7 Day 1 Inverse Relations and Functions.pdf
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77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
77 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
<strong>Day</strong> 1<br />
Objective:<br />
Find the inverse of a relation or function.<br />
Feb 2812:54 PM<br />
1
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Graph each pair of functions on a single coordinate plane.<br />
Feb 2812:56 PM<br />
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77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Activity: <strong>Inverse</strong>s<br />
Open your book to page 406 <strong>and</strong><br />
complete numbers 1 <strong>and</strong> 2 (ONLY)<br />
from the activity in your notes.<br />
Mar 110:31 AM<br />
3
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Mar 110:31 AM<br />
4
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Mar 110:31 AM<br />
5
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Mar 110:31 AM<br />
6
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
The <strong>Inverse</strong> of a Function<br />
If a relation pairs element a of its domain to element b of its range, the<br />
inverse relation pairs b with a.<br />
relation<br />
inverse<br />
(a, b) (b, a)<br />
The domain <strong>and</strong> range are reversed from the relation to the inverse.<br />
Example: Relation r <strong>Inverse</strong> of r<br />
Domain Range Domain Range<br />
1.2 1.2<br />
1<br />
1<br />
1.4 1.4<br />
1.6 2<br />
2 1.6<br />
1.9 1.9<br />
Feb 2812:57 PM<br />
7
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Example #1: Finding the <strong>Inverse</strong> of a Relation<br />
a. Find the inverse of relation s.<br />
Relation s<br />
x 1 2 3 4 x<br />
y 1 0 1 1 y<br />
<strong>Inverse</strong> of Relation s<br />
Feb 2812:58 PM<br />
8
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Example #1: Finding the <strong>Inverse</strong> of a Relation<br />
Relation s<br />
<strong>Inverse</strong> of Relation s<br />
x 1 2 3 4 x 1 0 1 1<br />
y 1 0 1 1 y 1 2 3 4<br />
b. Graph s <strong>and</strong> its inverse.<br />
Relation s<br />
<strong>Inverse</strong> of s<br />
Feb 2812:59 PM<br />
9
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Example #1: Finding the <strong>Inverse</strong> of a Relation<br />
c. Describe how the line y = x is related to the graphs<br />
of s <strong>and</strong> its inverse.<br />
d. Is relation s a function<br />
Is the inverse of s a function<br />
Relation s<br />
<strong>Inverse</strong> of s<br />
Feb 2812:59 PM<br />
10
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Get It Got It Good!<br />
The graph of the inverse of a relation is the<br />
reflection over the line y = x of the graph of<br />
the relation. If a relation or function is<br />
described by an equation in x <strong>and</strong> y, you can<br />
interchange x <strong>and</strong> y to get the inverse.<br />
Feb 2812:59 PM<br />
11
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Example #2: Interchanging x <strong>and</strong> y.<br />
a. Find the inverse of y = x 2 + 3.<br />
y = x 2 + 3<br />
x = y 2 + 3<br />
x 3 = y 2<br />
y = ±√x 3<br />
b. Is y = x 2 + 3 a function<br />
Is the inverse a function Explain.<br />
Feb 2812:59 PM<br />
12
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Example #2: Interchanging x <strong>and</strong> y.<br />
c. Graph y = x 2 + 3 <strong>and</strong> its inverse, y = ±√x 3<br />
Feb 2812:59 PM<br />
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77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Example #3: Interchanging x <strong>and</strong> y.<br />
a. Find the inverse of y = 3x 10.<br />
b. Is the inverse a function Explain.<br />
Feb 2812:59 PM<br />
14
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Example #3: Interchanging x <strong>and</strong> y.<br />
c. Graph y = 3x 10 <strong>and</strong> its inverse.<br />
Feb 2812:59 PM<br />
15
77 <strong>Day</strong> 1 <strong>Inverse</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
March 03, 2009<br />
Homework:<br />
page 410<br />
(1 20)<br />
Mar 111:14 AM<br />
16
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