7-7 Day 1 Inverse Relations and Functionsstaffweb.psdschools.org/kemotich/Mrs_Motichka/Algebra...
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77 Day 1 Inverse Relations and Functions 1 March 03, 2009 Feb 2812:54 PM 77 Inverse Relations and Functions Day 1 Objective: Find the inverse of a relation or function.
Transcript of 7-7 Day 1 Inverse Relations and Functionsstaffweb.psdschools.org/kemotich/Mrs_Motichka/Algebra...
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77 Inverse Relations and FunctionsDay 1
Objective: Find the inverse of a relation or function.
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Graph each pair of functions on a single coordinate plane.
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Activity: InversesOpen your book to page 406 and complete numbers 1 and 2 (ONLY)
from the activity in your notes.
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The Inverse of a FunctionIf a relation pairs element a of its domain to element b of its range, the inverse relation pairs b with a.
relation inverse (a, b) (b, a)
The domain and range are reversed from the relation to the inverse.
Example: Relation r Inverse of r
Domain Range Domain Range 1.2 1.2 1.4 1.4 1.6 1.6 1.9 1.9
1
2
1
2
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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 x y 1 0 1 1 y
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Example #1: Finding the Inverse of a Relation Relation s Inverse of Relation s
x 1 2 3 4 x 1 0 1 1 y 1 0 1 1 y 1 2 3 4
b. Graph s and its inverse.
Relation s Inverse of s
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Relation sInverse of s
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?
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Get It? Go
t It? Good!
The graph
of the inve
rse of a re
lation is th
e
reflection o
ver the line
y = x of th
e graph of
the relation
. If a relat
ion or fun
ction is
described
by an equa
tion in x an
d y, you ca
n
interchang
e x and y to
get the in
verse.
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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 3b. Is y = x2 + 3 a function? Is the inverse a function? Explain.
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Example #2: Interchanging x and y.
c. Graph y = x2 + 3 and its inverse, y = ±√x 3
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Example #3: Interchanging x and y.
a. Find the inverse of y = 3x 10.
b. Is the inverse a function? Explain.
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Example #3: Interchanging x and y.
c. Graph y = 3x 10 and its inverse.
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Homework:page 410 (1 20)
