Rational Function Graphing

Rational Function Graphing

1. 1. Domain

   • Everything except values that make the denominator = 0
   • Ex. 3x/x+10
     • Domain: x=all real numbers except -10

2. 2. X Intercepts

   • Set f(x)=0, solve for x
   • Ex. 3x/x+10
     • X Intercept=(0,0)

3. 3. Y Intercepts

   • Set x=0, then solve
   • Ex. 3x/x+10
     • Y Intercept=(0,0)

4. 4. Horizontal Asymptotes

   • Compare degrees of numerator and denominator
     • If top=bottom: Ratio of leading exponents
     • If bottom>top: y=0
     • If top>bottom: No horizontal asymptotes
   • Ex. 3x/x+10
     • Horizontal Asymptote=(y=3)

5. 5. Vertical Asymptotes

   • Simplify polynomial then find the zeroes of the denominator
   • Ex. 3x/x+10
     • Vertical Asymptotes=(x=-10)

6. 6. Plot Additional Points

   • Plug x values into function, plot the points that come out of it
   • Ex.
     • f(2)=3x/x+10
     • f(-3)=3x/x+10

7. Graphed Examples

   • f(x)=4/x
     • Domain: x≠0, No x intercept, No y intercept, V. Asymptote x=0, H. Asymptote y=0
   • Domain: All real numbers, x/y intercept (0,0), H. Asymptote: y=0, V. Asymptote: None

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