1.7

Topic

Rational Functions and End Behavior

Practice by unit: Polynomial and Rational Functions

Sub-standards

• 1.7.A.4 — Describe end behaviors of rational functions. If neither polynomial in a rational function dominates the other for input values of large magnitude, then the quotient of the leading terms is a constant, and that constant indicates the location of a horizontal asymptote of the graph of the original rational function.
• 1.7.A.5 — If the polynomial in the denominator dominates the polynomial in the numerator for input values of large magnitude, then the quotient of the leading terms is a rational function with a constant in the numerator and nonconstant polynomial in the denominator, and the graph of the original rational function has a horizontal asymptote at y = 0.
• 1.7.A.6 — When the graph of a rational function r has a horizontal asymptote at y = b, where b is a constant, the output values of the rational function get arbitrarily close to b and stay arbitrarily close to b as input values increase or decrease without bound. The corresponding mathematical notation is lim r x( ) = b or x lim r x( ) = b. x UNIT 1