Subtracting functions

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  1. Determine the Difference of Two Functions Algebraically
    If f(x)=5x3x+6f(x)= 5x^3-x+6
    1. (fg)(x)(f-g)(x)
    2. (gf)(x) (g-f)(x)
    3. (gf)(2) (g-f)(-2)
      evaluate in two different ways
  2. Determine the Difference of Two Functions Graphically
    Given the graphs of functions f(x)f(x)
    and g(x)g(x)

    Subtraction of functions
    1. sketch: (gf)(x)(g-f)(x)
    2. evaluate:
      iii) (gf)(4)(g-f)(4)
  3. Determine the Difference of Two Functions Point-by-Point
    The graph of y=f(x)y=f(x)
    includes the points (2,5),(4,15),(7,30)
    The graph of y=g(x)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=(fg)(x)?y=(f-g)(x)?
    1. (0,1) (0,-1)
    2. (0,1) (0,1)
    3. (2,1) (2,-1)
    4. (3,30) (3,30)
Topic Notes
subtracting functions: (fg)(x)=f(x)g(x)(f-g)(x) = f(x)-g(x)