text: # Domain, zeroes, and graphing to check the function
  
  #### thebestrose828
  
  Hey,
  I really need help solving this question. If someone could provide a step-by-step guide? The question asks for the domain of the function, zeroes, and to graph it to check the function.
  The function is as follows:
  x3 +x2-2x
  _________=f(x)
  2x3-x2-6x
  
  (The above is supposed to be those two equations divided by each other equals f(x), not really that computer savvy with typing math stuff)
  
  Last edited:
  
  #### skeeter
  
  MHF Helper
  start by factoring numerator & denominator ...
  
  $f(x) = \dfrac{x(x+2)(x-1)}{x(2x+3)(x-2)}$
  
  note that the numerator & denominator have a common factor of $x$ ... this indicates a point discontinuity (a "hole") at $(0,1/3)$, also indicating the absence of a y-intercept.
  
  vertical asymptotes where $2x+3=0 \implies x = -\dfrac{3}{2}$ and where $x-2=0 \implies x = 2$
  
  so, domain is all real values of $x$ except $x=0$, $x=-\dfrac{3}{2}$, and $x=2$
  
  horizontal asymptote is determined by the ratio of the leading coefficients, $y = \dfrac{1}{2}$
  
  zeros where $x+2=0 \implies x=-2$ and $x-1=0 \implies x=1$
  
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