Section 2.2 Domain and Range

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Section 2.2Domain and Range
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• Consider problem 22 from last class
• A ball is thrown up from the ground with an
  initial velocity 64 ft/sec. Its height at time t
  is
• What input values yield an output?
• Give them all
• What are all of the possible outputs?

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Definition

• If Q f(t), then
• The domain of f is the set of input values, t,
  which yield an output value
• The range of f is the corresponding set of output
  values, Q
• When a function is used to model a real
  situation, it may be necessary to modify the
  domain and range (as in the prior example)

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Using a graph to find domain and range

• Lets take a look at the graph of
• This function gives the height, h, of a sunflower
  plant over t days
• Lets look at the first 100 days
• What is its domain?
• What is its range?

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Using a formula to find domain and range

• Consider
• Remember, the domain is all real numbers except
  those that do not yield an output
• All real except x ? 0
• Remember, the range is all real numbers that the
  formula can return as output values
• y -1

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• We have three major cases to worry about with
  domain
• Cannot have 0 in the denominator
• Cannot have a negative number under a radical
• Cannot take log or ln of 0 or a negative number
• Consider
• Domain x gt -7
• Range y gt 0

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• In your groups work on problems 3, 7, 11, 15, 23,
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