A. Definitions

Rational Equation  an equation in the form of y = (a/b), where a and b are polynomials and b ≠ 0.

Simple Rational Equation  given y = (a/b), a and b are linear.

Given
 The graph is a hyperbola.
 The asymptotes are x = h and y = k.
 The domain is all real numbers except h.
 The range is all real numbers except k.

Given
 The vertical asymptote goes through the xvalue that makes the denominator zero.
 The horizontal asymptote goes through the yvalue equal to (a/c).
 The domain is all real numbers except the xvalue that makes the denominator zero.
 The range is all real numbers except y = (a/c).
B. Steps for Graphing Simple Rational Equations
 Determine and sketch the vertical asymptote.
 Determine and sketch the horizontal asymptote.
 Graph two points on the left and right side of the vertical asymptote.
 Choose two xvalues that are smaller and two that are larger than the xvalue the vertical asymptote goes through.
 Substitute each xvalue into the equation to determine the yvalues.
 Connect the points to determine the hyperbolas.
