B. Steps for Graphing Simple Rational Equations
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.
- 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.
- The vertical asymptote goes through the x-value that makes the denominator zero.
- The horizontal asymptote goes through the y-value equal to (a/c).
- The domain is all real numbers except the x-value that makes the denominator zero.
- The range is all real numbers except y = (a/c).
- 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 x-values that are smaller and two that are larger than the x-value the vertical asymptote goes through.
- Substitute each x-value into the equation to determine the y-values.
- Connect the points to determine the hyperbolas.