Sullivan%20Algebra%20and%20Trigonometry:%20Section%20R.2%20Algebra%20Review

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Sullivan Algebra and Trigonometry Section
R.2Algebra Review

• Objectives of this Section
• Graph Inequalities
• Find Distance on the Real Number Line
• Evaluate Algebraic Expressions
• Determine the Domain of a Variable
• Use the Laws of Exponents
• Evaluate Square Roots
• Use a Calculator to Evaluate Exponents
• Use Scientific Notation

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The Real Number Line
The negative real numbers are the coordinates of
points to the left of the origin 0.
The real number zero is the coordinate of the
origin O.
The positive real numbers are the coordinates of
points to the right of the origin O.
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Comparing the position of two numbers on the
number line is done using inequalities.
a lt b means a is to the left of b
a b means a and b are at the same location
a gt b means a is to the right of b
Inequalities can also be used to describe the
sign of a real number.
a gt 0 is equivalent to a is positive.
a lt 0 is equivalent to a is negative.
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If P and Q are two points on a real number line
with coordinates a and b, respectively, the
distance between P and Q, denoted by d (P, Q), is
Example Find the distance between 3 and 2 on
the number line.
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Recall, letters such as x, y, z, a, b, and c are
used to represent numbers. If the letter is used
to represent any number from a given set of
numbers, it is called a variable.
The set of values that a variable may assume is
called the domain of the variable.
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Example of Domain
The result is read The set of all real numbers z
such that z is not equal to 3
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Exponents Basic Definitions
If a is a real number and n is a positive integer,
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Examples
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Laws of Exponents
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Example
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Example
Simplify the expression. Express the answer so
only positive exponents occur.
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Absolute Value is needed here, since the
principal square root produces a positive value.
Example
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Using your calculator
For Scientific Calculators
Evaluate
Keystrokes
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3.4

133.6336
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Converting a Decimal to Scientific Notation
1. Count the number N of places that the decimal
point must be moved in order to arrive at a
number x, where 1 lt x lt 10.
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Examples Scientific Notation
Write the number 5,100,000,000 in scientific
notation.
Write the number 0.00032 in scientific notation.
Solution 0.000043