Interval Notation, Exponents and Radicals

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Interval Notation, Exponents and Radicals
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Interval Notation

• When given a time period or interval of values,
  we often use inequality notation
  to describe the portion of the graph in
  which we are interested.
• In calculus, inequality notation is rarely used.
  More often we use interval notation to describe
  the portion of the graph.

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Brackets vs. Parenthesis

• When using interval notation the smaller number
  always comes first.
• If we want to include the number (greater than or
  equal to) we use a bracket. If we do not want to
  include the number (greater than ___), we use
  parenthesis.

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Examples

• Write in interval notation.
• Write in interval notation.
• Write in interval notation.

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Unbounded Intervals

• Write in interval notation.
• Write in interval notation.

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Laws of Exponents

• When _________ bases, ______ exponents.
• When _________ bases, _______ exponents.

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1. When a monomial with different bases is raised to
   a power, the exponent must be applied to ______
   bases.
2. When a power is raised to another power,
   ___________ the exponents.

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Powers that are negative or zero

• Any base that is raised to the power of
  zero ____.
• To make a negative exponent become positive,
  ______ _____ base and change the sign of the
  exponent.

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Common Sense Rules

• If , then __________.
• If , then __________.

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Exponents Examples

• Simplify
• 2) Simplify

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Properties of Radicals

• We cannot add or subtract radicals if the
  radicand is not the same.

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Examples

• Simplify
• Write as a rational exponent

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Rationalizing Radicals

1. Simplify
2. Rationalize the numerator

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Homework

• Pg. 10 (19 27 odd, 31 35 odd)
• Pg. 23 (15 23 odd, 35 43 odd, 49 53odd, 61
  67 odd, 73, 75)