Dividing functions

Lessons

• 1.
  Determine the Quotient of Two Functions and State Its Domain
  Write an expression in the simplest form for $(\frac{f}{g})(x)$
  State the domain restrictions
  a)

  $f(x)=3x-8$

  $g(x)=x+2$
  
  
  
  b)

  $f(x)=4x^3+5x^2$

  $g(x)=x$
  
  
  
  c)

  $f(x)=2x^2+4x-30$

  $g(x)=2x-6$
  
  
  
  d)

  $f(x)=x-3$

  $g(x)=x^2+2x-15$
  
  
  

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• 2.
  Operations of Functions – In a Nutshell
  Consider the functions $f(x)=\frac{x}{x+5}$

  and $g(x)=\frac{3x}{x-2}$
  
  a)

  state the domain of $f(x)$

  and $g(x)$
  
  
  
  b)

  write an expression in the simplest form for each
  of the following and state the domains
  

  i) $(f+g)(x)$
  

  ii) $(f-g)(x)$
  

  iii) $(fg)(x)$
  

  iv) $(\frac{f}{g})(x)$
  
  
  
  c)

  evaluate $(\frac{f}{g})(4)$

  in 2 different ways
  
  
  

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• 3.
  Sketch the Quotient of Two Functions
  Consider the functions $f(x)=2x^2+4x-30$
  

  $g(x)=20x-60$
  
  a)

  Determine the equation of the function
  $h(x)=(\frac{g}{f})(x)$ and state the domain restrictions
  
  
  
  b)

  Sketch the graph of

  $h(x)=(\frac{g}{f})(x)$
  
  

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