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Rational Function Graphing

Description

Mind Map on Rational Function Graphing, created by Benjamin Mark Cottam on 17/11/2015.
Benjamin Mark Cottam
Mind Map by Benjamin Mark Cottam, updated more than 1 year ago
Benjamin Mark Cottam
Created by Benjamin Mark Cottam over 9 years ago
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Resource summary

Rational Function Graphing
  1. 1. Domain
    1. Everything except values that make the denominator = 0
      1. Ex. 3x/x+10
        1. Domain: x=all real numbers except -10
      2. 2. X Intercepts
        1. Set f(x)=0, solve for x
          1. Ex. 3x/x+10
            1. X Intercept=(0,0)
          2. 3. Y Intercepts
            1. Set x=0, then solve
              1. Ex. 3x/x+10
                1. Y Intercept=(0,0)
              2. 4. Horizontal Asymptotes
                1. Compare degrees of numerator and denominator
                  1. If top=bottom: Ratio of leading exponents
                    1. If bottom>top: y=0
                      1. If top>bottom: No horizontal asymptotes
                      2. Ex. 3x/x+10
                        1. Horizontal Asymptote=(y=3)
                      3. 5. Vertical Asymptotes
                        1. Simplify polynomial then find the zeroes of the denominator
                          1. Ex. 3x/x+10
                            1. Vertical Asymptotes=(x=-10)
                          2. 6. Plot Additional Points
                            1. Plug x values into function, plot the points that come out of it
                              1. Ex.
                                1. f(2)=3x/x+10
                                  1. f(-3)=3x/x+10
                                2. Graphed Examples
                                  1. f(x)=4/x
                                    1. Domain: x≠0, No x intercept, No y intercept, V. Asymptote x=0, H. Asymptote y=0
                                    2. Domain: All real numbers, x/y intercept (0,0), H. Asymptote: y=0, V. Asymptote: None
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