Subtracting functions

Lessons

• 1.
  Determine the Difference of Two Functions Algebraically
  If $f(x)= 5x^3-x+6$

  and

  $g(x)=4x-8,$
  Determine:
  a)

  $(f-g)(x)$
  
  
  
  b)

  $(g-f)(x)$
  
  
  c)

  $(g-f)(-2)$

  evaluate in two different ways
  
  

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• 2.
  Determine the Difference of Two Functions Graphically
  Given the graphs of functions $f(x)$

  and $g(x)$
  
  
  
  a)

  sketch: $(g-f)(x)$
  
  
  
  b)

  evaluate:
  

  i)

  $(g-f)(-3)$
  

  ii)

  $(g-f)(0)$
  

  iii) $(g-f)(4)$
  
  
  

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• 3.
  Determine the Difference of Two Functions Point-by-Point
  The graph of $y=f(x)$

  includes the points (2,5),(4,15),(7,30)
  The graph of $y=g(x)$

  includes the points (2,6),(3,16),(4,30)
  If f and g are defined for all real values of x , then which of the
  following points must lie on the graph of $y=(f-g)(x)?$
  
  a)

  $(0,-1)$
  
  
  
  b)

  $(0,1)$
  
  
  
  c)

  $(2,-1)$
  
  
  
  d)

  $(3,30)$
  
  

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