Introduction to Rational Expressions and Functions

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Introduction to Rational Expressions and Functions

• Section 7.1

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Definitions
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Rational Functions/Restricted Values
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What do we notice?

• The graph has two branches.
• Because no point of the graph has an x-coordinate
  of 0, there is a break at x 0 and the branches
  are not connected.
• We may draw a vertical line to show this break
  specifically, that the graph approaches this
  line, but neither reaches it or crosses it.
• The line is called a VERTICAL ASYMPTOTE.
• Because of this break, the number 0 is NOT part
  of the domain of the function.

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Using the Graphing Calculator
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Example
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Excluded/Restricted Values
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Restricted (Excluded) Values

• The previous example illustrates that the number
  5 was NOT part of the domain of the function. WHY
  NOT?
• To determine the domain of a rational function we
  need to determine the values of the variable for
  which the denominator is 0.
• Set the denominator equal to 0 and solve for the
  variable.
• The solutions of this equation are NOT part of
  the domain of the function and MUST be excluded.

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Examples
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Simplifying Rational Expressions

• To SIMPLIFY a rational expression is comparable
  to reducing a fraction to lowest terms.
• First, lets simplify the fraction
• We will factor both the numerator and the
  denominator and look for factors of one.

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Canceling ?
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Simplifying (contd)
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Examples
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Examples (contd)