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Basics of functions continued
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Basics of functions continued

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Transcript

  • 1. Basics of Functions Continued…
    • Domain
    • Evaluating from…
      • An equation
      • A graph
      • A table
    • Composition
      • Add/Subtract/Multiply/Divide
      • Difference Ratio
  • 2. Domain
  • 3.  
  • 4.  
  • 5.  
  • 6.  
  • 7.  
  • 8.  
  • 9.
    • 6. Given the graph, if possible, evaluate (f + g)(1).
    • f(1) = (think when x = 1 on the f(x) graph, what is the y-value?)
    • g(1) = (think when x = 1 on the g(x) graph, what is the y-value?)
    • (f + g)(1) = add the two parts above together
    – 4 – 2 2 5 0 9 4 a. x y
  • 10.
    • 6. Given the graph, evaluate (f + g)(1).
    • f(1) = 3 g(1) = 1
    • (f + g)(1) = 4
    – 4 – 2 2 5 0 9 4 a. x y
  • 11.
    • 7. Given the graph, if possible, evaluate (f / g)(0).
    • f(0) = (think when x = 0 on the f(x) graph, what is the y-value?)
    • g(0) = (think when x = 1 on the g(x) graph, what is the y-value?)
    • (f / g)(0) = divide
    – 4 – 2 2 5 0 9 4 x y
  • 12.
    • 7. Given the graph, evaluate (f / g)(0).
    • f(0) = 1
    • g(0) = 0
    • (f /g)(0) = 1/0, thus (f/g)(0) is undefined because the denominator
    • is 0.
    – 4 – 2 2 5 0 9 4 x y
  • 13.
    • 8. Given the table, if possible, use the given representations of f and g to evaluate (f · g)(1).
    • f(1), when x = 1 in the table, what is the value of f(x)?
    • g(1), when x = 1 in the table,
    • what is the value of g(x)?
    • (f · g)(1), evaluate the product
    x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2
  • 14.
    • 8. Given the table, if possible, use the given representations of f and g to evaluate (f · g)(1).
    • f(1) = 3
    • g(1) = 1
    • (f · g)(1) = 3(1)
    • = 3
    x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2
  • 15.
    • 9. Given the table, if possible, use the given representations of f and g to evaluate (f – g)(-2).
    • f(-2), when x =-2 in the table, what is the value of f(x)?
    • g(-2), when x = -2 in the table,
    • what is the value of g(x)?
    • (f – g)(-2), evaluate the difference
    x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2
  • 16.
    • 9. Given the table, if possible, use the given representations of f and g to evaluate (f – g)(-2).
    • f(-2) = -3
    • g(-2) = undefined
    • (f – g)(-2) = undefined
    • Note: looking back at the graph on slide 7, g(x) is not
    • defined at x = -2. In simplistic
    • terms, that means there is no graph for the value of x.
    x  ( x ) g ( x ) – 2 – 3 undefined 0 1 0 1 3 1 -1 -1 undefined 4 9 2