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
   1. $f(x)=3x-8$
      $g(x)=x+2$
      
   2. $f(x)=4x^3+5x^2$
      $g(x)=x$
      
   3. $f(x)=2x^2+4x-30$
      $g(x)=2x-6$
      
   4. $f(x)=x-3$
      $g(x)=x^2+2x-15$
      
2. Operations of Functions – In a Nutshell
   Consider the functions $f(x)=\frac{x}{x+5}$
   and $g(x)=\frac{3x}{x-2}$
   
   1. state the domain of $f(x)$
      and $g(x)$
      
   2. 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) $(\frac{f}{g})(x)$
      
   3. evaluate $(\frac{f}{g})(4)$
      in 2 different ways
      
3. Sketch the Quotient of Two Functions
   Consider the functions $f(x)=2x^2+4x-30$
   
   $g(x)=20x-60$
   
   1. Determine the equation of the function
      $h(x)=(\frac{g}{f})(x)$ and state the domain restrictions
      
   2. Sketch the graph of
      $h(x)=(\frac{g}{f})(x)$