Algebra II Recipe: Graphing Simple Rational Functions

A. Definitions

1. Rational Equation - an equation in the form of y = (a/b), where a and b are polynomials and b ≠ 0.
2. Simple Rational Equation - given y = (a/b), a and b are linear.
3. Given
   1. The graph is a hyperbola.
   2. The asymptotes are x = h and y = k.
   3. The domain is all real numbers except h.
   4. The range is all real numbers except k.
4. Given
   1. The vertical asymptote goes through the x-value that makes the denominator zero.
   2. The horizontal asymptote goes through the y-value equal to (a/c).
   3. The domain is all real numbers except the x-value that makes the denominator zero.
   4. The range is all real numbers except y = (a/c).

B. Steps for Graphing Simple Rational Equations

1. Determine and sketch the vertical asymptote.
2. Determine and sketch the horizontal asymptote.
3. Graph two points on the left and right side of the vertical asymptote.
   1. Choose two x-values that are smaller and two that are larger than the x-value the vertical asymptote goes through.
   2. Substitute each x-value into the equation to determine the y-values.
4. Connect the points to determine the hyperbolas.

Practice Problems