Rational Functions

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Chapter 7

• Section 1
• Rational Functions

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Definitions
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Examples
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The graph of f(x) 1/x

• Load into y1
• Look at the table of values

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End Behavior

• As x approaches positive infinity, f(x)1/x is
  going to 0
• As x approaches negative infinity, f(x)1/x is
  going to 0

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Origin Behavior

• As x approaches positive 0, f(x)1/x is going to
  positive infinity
• As x approaches negative 0, f(x)1/x is going to
  negative infinity

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Asymptotes

• If a function approaches a fixed value but never
  ever gets there, we say that the fixed value is
  an asymptote.
• In the graph of f(x) 1/x the x-axis is a
  horizontal asymptote.
• In the graph of f(x) 1/x the y-axis is a
  vertical asymptote.

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Lets Translate

• Recall what happens to the graph of a function
  when we replace x with x h?
• For example

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So

• What happens to
• If we rewrite it as

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Make a Sketch
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Lets Translate

• Recall what happens to the graph of a function
  when we replace f(x) with f(x)k For example

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So

• What happens to
• If we rewrite it as

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Domain and Range

• Find the domain and range of

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Reflections

• Compare
• To the graph of

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Examples

• Page 615
• 1, 3, 8, 12 (Make sketches now, no graph paper
  needed until HW), 23, 25, 33, 43