ACT Test Prep I-2

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ACT Test Prep I-2

• 3x³ 2x²y 4x²y is equivalent to
• F. 9x7y²
• G. 9x¹²y²
• H. 24x7y²
• J. 24x¹²y
• K. 24x¹²y²

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1.2Composition of Functions
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Operations with Functions

• Sum
• Difference
• Product
• Quotient

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Example 1

• Given f(x) 2x 1 and g(x) x², find each
  function.
• (f g) (x)
• (f - g) (x)
• (f g) (x)
• d.

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More examples

• Given f(x) 3x² 4x 5 and g(x) 2x 9, find
  each function.
• (f g) (x)
• (f - g) (x)
• (f g) (x)
• d.

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• For the Lotsa Coffee Shop, the revenue r(x) in
  dollars from selling x cups of coffee is
  r(x)1.5 x.
• The cost c(x) for making and selling the coffee
  is c(x) 0.2x 110.
• Write the profit function
• Profit function revenue cost p(x) r(x)
  c(x)
• Find the profit on 100, 200, and 500 cups of
  coffee sold.

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Composition of Functions

• The term "composition of functions"
• (or "composite function") refers to the
  combining of functions in a manner where the
  output from one functionbecomes the input for
  the next function.
• In math terms,
• the range (the y-value answers) of one function
  becomesthe domain (the x-values) of the next
  function 

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• The notation used for composition is
• (f ?g) (x) f (g(x))
• and is read
• "f composed with g of x" or "f of g of x".
• Notice how the letters stay in the same order in
  each expression for the composition. f (g(x)) cle
  arly tells you to start with function g (innermost
  parentheses are done first).

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Examples

• Find (f ? g)(x) and (g ? f)(x) for each f(x) and
  g(x).
• f(x) 2x 5
• g(x) 3 x
• f(x) 2x 3
• g(x) x² - 2x
• 3. f(x) x² - 2x
• g(x) 3x

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Domains of a Composition

• The domain of a composed function (f ? g)(x) is
  determined by the domains of f(x) and g(x).
• For example
• State the domain of (f ? g)(x) for
• f(x)
• g(x)

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• State the domain of (f ? g)(x) for
• f(x) g(x) x 3
• f(x) g(x) 7 - x

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Assignment

• Pages 17 -18
• 12 24 even
• 39
• Write the functions of each problem and show all
  work.