2.3 The Algebra of Functions

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2.3 The Algebra of Functions

• When finding the domain of a function from an
  equation, we must exclude real numbers that cause
  division by _______________ (no zeros in the
  denominator) and real numbers that result in a
  square root of a ______________ number (this
  results in imaginary numbers).

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Example 1

• Find the domain of each function
• A) f(x) ½ x 3
• B) g(x) 7x 4
• x 5

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• We can add (find the _______________), subtract
  (find the _______________), multiply (find the
  _______________), and divide (find the
  _______________) functions.
• Remember when we divide functions, the
  denominator cannot be 0!

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Example 2

• Let f(x) 3x2 4x 1 and g(x) 2x
  7. Find each of the following
• A) (f g)(x)
• B) (f g)(4)

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Example 3

• Let f(x) 5 and g(x) 7 .
• x
  x 8
• Find each of the following
• A) (f g)(x)

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Example 3 continued . . .

• B) the domain of f g.

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Example 4

• Let f(x) x2 2x and g(x) x 3.
  Find each of the following
• A) (f g)(5)
• B) (f g)(x) and (f g)(-1)

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Example 4 continued . . .

• C) (f/g)(x) and (f/g)(7)
• D) (fg)(-4)

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Example 5

• Birth model B(x) 7.4x2 15x 4046
• Death model D(x) -3.5x2 20x 2405
• A) Write a function that models the total number
  of births and deaths in the United States for
  each year from 2000 through 2005.

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Example 5 continued . . .

• B) Use the function from part(a) to find the
  total number of births and deaths in the United
  States in 2005.
• C) Does the result in part(b) overestimate or
  underestimate the actual number of total births
  and deaths in 2005 obtained from the data in
  Figure 2.15 on page 117? By how much?

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Homework

• Pages 122-124
• 1 61 every other odd
• 16 total