Rational Function Graphing

1. Domain
1. Everything except values that make the denominator = 0
2. Ex. 3x/x+10
  1. Domain: x=all real numbers except -10
2. X Intercepts
1. Set f(x)=0, solve for x
2. Ex. 3x/x+10
  1. X Intercept=(0,0)
3. Y Intercepts
1. Set x=0, then solve
2. Ex. 3x/x+10
  1. Y Intercept=(0,0)
4. Horizontal Asymptotes
1. Compare degrees of numerator and denominator
  1. If top=bottom: Ratio of leading exponents
  2. If bottom>top: y=0
  3. If top>bottom: No horizontal asymptotes
2. Ex. 3x/x+10
  1. Horizontal Asymptote=(y=3)
5. Vertical Asymptotes
1. Simplify polynomial then find the zeroes of the denominator
2. Ex. 3x/x+10
  1. Vertical Asymptotes=(x=-10)
6. Plot Additional Points
1. Plug x values into function, plot the points that come out of it
2. Ex.
  1. f(2)=3x/x+10
  2. f(-3)=3x/x+10
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

Resumen del Recurso

	Creado por Benjamin Mark Cottam hace alrededor de 10 años