Algebra II Mr. Gilbert

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Algebra IIMr. Gilbert

• Chapter 7.8
• Inverse Functions and Relations
• Standard Honors

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Agenda

• Warm up
• Homework Review
• 7.7 Operations on Functions
• Lesson
• Homework

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Transparency 8
Click the mouse button or press the Space Bar to
display the answers.
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Transparency 8a
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Homework Review
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Communicate Effectively

• Domain Range
• Inverse Relation see below
• Inverse Function f(x), f-1(x)
• Identity Function I(x)x

Two relations in an inverse if and only if
whenever one contains (a,b) then the other
contains (b,a). this means all elements are
included
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Lesson 8 Contents
7.8 Inverse Functions and Relations
Example 1 Find an Inverse Relation (3) Example
2 Find an Inverse Function (5) Example 3 Verify
Two Functions are Inverses (3)
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Example 8-1a
Geometry The ordered pairs of the relation (1,
3), (6, 3), (6, 0), (1, 0) are the coordinates
of the vertices of a rectangle. Find the inverse
of this relation and determine whether the
resulting ordered pairs are also the coordinates
of the vertices of a rectangle.
To find the inverse of this relation, reverse the
coordinates of the ordered pairs. The inverse of
the relation is (3, 1), (3, 6), (0, 6), (0, 1).
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Example 8-1b
Answer Plotting the points shows that the
ordered pairs also describe the vertices of a
rectangle. Notice that the graph of the relation
and the inverse are reflections over the graph of
y x.
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Example 8-1c
Geometry The ordered pairs of the relation (3,
4), (1, 5), (2, 3), (1, 1), (2, 1) are the
coordinates of the vertices of a pentagon. Find
the inverse of this relation and determine
whether the resulting ordered pairs are also
the coordinates of the vertices of a pentagon.
Answer (4, 3), (5, 1), (3, 2), (1, 1), (1,
2)These ordered pairs also describe the
vertices of a pentagon.
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Example 8-2a
Step 1 Replace f (x) with y in the original
equation.
Step 2 Interchange x and y.
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Example 8-2b
Step 3 Solve for y.
Step 4 Replace y with f 1(x).
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Example 8-2d
Graph the function and its inverse.
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Example 8-2e
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Example 8-2f
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Example 8-3a
Check to see if the compositions of f (x) and g
(x) are identity functions.
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Example 8-3b
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Example 8-3c
Answer The functions are inverses since both
compositions equal x.
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Homework - Honors
See Syllabus 7.8 pp. 393-394 18, 20-36 even,
38-44
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Homework
See Syllabus 7.8 PP 393-394 14-36 even, 38-43.