Strategy For Graphing Polynomials And Rational Functions

1
Strategy For Graphing Polynomials And
Rational Functions

• 1. State the domain.
• 2. Find the Y-Intercept (x0) and the
  X- Intercept (y0) the easy ones in particular.
  
• You can use the synthetic division to find
  the easy zeros for the given polynomial
  function.
• 3. For rational functions ONLY, find the
  asymptotes.
• 4. Find Y and find the critical points.
• 5. Perform the sign analysis.
• 6. Graph the function.

2
AsymptotesFor Rational Functions

• 1. Vertical Asymptote
• Whatever makes the denominator zero is your
  vertical asymptote, as long as you do not have
  0/0. Remember 0/0 could have a limit and it
  simply means a hole in the graph.
• 2. Horizontal And Slant Asymptote
• Is the limit of the rational function as

3
Horizontal SlantAsymptotes

• If the power of the numerator is the same as the
  power of the denominator, then the horizontal
  asymptote is y the ratio of the leading
  coefficients.
• If the power of the numerator is less than the
  power of the denominator, then the horizontal
  asymptote is y0.
• If the power of the numerator is greater than the
  power of the denominator by one degree, then the
  slant asymptote is y the quotient of the
  division.
• Here the synthetic division can prove useful.
• Notice that you can not have horizontal and slant
  asymptotes at the same time.