Subtracting functions

Lessons

1. Determine the Difference of Two Functions Algebraically
   If $f(x)= 5x^3-x+6$
   and
   $g(x)=4x-8,$
   Determine:
   1. $(f-g)(x)$
      
   2. $(g-f)(x)$
   3. $(g-f)(-2)$
      evaluate in two different ways
2. Determine the Difference of Two Functions Graphically
   Given the graphs of functions $f(x)$
   and $g(x)$
   
   
   
   1. sketch: $(g-f)(x)$
      
   2. evaluate:
      
      i)
      $(g-f)(-3)$
      
      ii)
      $(g-f)(0)$
      
      iii) $(g-f)(4)$
      
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 $y=(f-g)(x)?$
   
   1. $(0,-1)$
      
   2. $(0,1)$
      
   3. $(2,-1)$
      
   4. $(3,30)$