Math 30 College Algebra January 31, 2000

1
Math 30 --- College AlgebraJanuary 31, 2000

• Section 1.6 questions
• Section 1.7
• Assignment 8
• Break
• Section 1.8
• Assignment 9

2
AnnouncementsJanuary 31, 2000

• Section 1.3, 1.4, and 1.5 due
• Exam 1 Wednesday
• bring scantron, calculator, graph paper,
  pencil and eraser
• Distance Students --- Contact me for exam time
  and place.

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Tests for Symmetry
x-axis Replace y by -y in the equation. If an
equivalent equation results, the graph of the
equation is symmetric with respect to the
x-axis. y-axis Replace x by -x in the equation.
If an equivalent equation results, the graph of
the equation is symmetric with respect to the
y-axis.
4
Tests for Symmetry
Origin Replace x by -x and y by -y in the
equation. If an equivalent equation results, the
graph of the equation is symmetric with respect
to the origin.
5
Even and Odd Functions

• A function f is even for every number x in its
  domain the number -x is also in the domain and
• A function f is odd for every number x in its
  domain the number -x is also in the domain and

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Even and Odd Functions

• The graph of an even function is symmetric about
  the y-axis.
• The graph of an odd function is symmetric about
  the origin.

7
Graphing Transformations
Given the graph of the function . The
graph of is the graph of shifted
horizontally h units. The graph of is the
graph of shifted vertically k units.
8
Graphing Reflections
Given the graph of the function . The
graph of is the graph of reflected across
the y-axis. The graph of is the graph of
reflected across the x-axis.
9
Compressions and Stretches
Given the graph of the function . The
graph of is a horizontal stretch/compression
of the graph of The graph of is a
vertical stretch/compression of the graph of
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Algebra of Functions
Addition Subtraction Multiplication Division
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Composition of Functions
The composite function , the composition of
and is defined as where is in the domain
of and is in the domain of .
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Assignments 8 and 9

• Read 2.1- 2.2 for Monday
• Bring questions for the exam.
• Homework 1.7 pbs 5-35 (every 5th), 47, 49, 51,
  52-55, 58-65, 67, 73, 74, 77-80
• Homework 1.8 pbs 3, 5, 7, 15, 19, 29, 33, 35,
  39, 47, 55-58, 70-74