Vocabulary
End Behavior- The behavior of the graph of a function as x approaches positive infinity (+∞) or negative infinity (-∞).
Asymptote- A line that a graph approaches more and more closely.
Rational Function- A function in the form f(x)= p(x)/q(x) , where p(x) and q(x) are polynomials and q(x)≠0.
Asymptote- A line that a graph approaches more and more closely.
Rational Function- A function in the form f(x)= p(x)/q(x) , where p(x) and q(x) are polynomials and q(x)≠0.
Essential Information
P(x) and q(x) are polynomials with no common factors other than ±1. The graph of the flowing rational function has the characteristics listed below.
- The x-intercepts of the graph f are the real zeros of P(X).
- The graph of f has a vertical asymptote at each real zero of q(x)
- The graph of f has at most one horizontal asymptote, which is determined by the degrees m and n of (p(x) and q(x)