Unit 2 · 4 lessons
Rational Functions
What happens when a variable sits in the denominator: reciprocals, vertical and horizontal asymptotes, holes, full sketches, and solving rational equations and inequalities.
- 37 practice questions
- 29 flashcards
- 3 interactive lessons
Lessons
- 1Reciprocal FunctionsFlip a linear or quadratic function upside down and watch what happens: big values become tiny, zeros become vertical asymptotes, and the points where the function equals or never move.Interactive9 questions
- 2Restrictions, Asymptotes and HolesEvery rational function is a ratio of polynomials. Factor it, state the restrictions, then decide which restrictions are vertical asymptotes and which are holes — and read the end behaviour off the degrees.Interactive9 questions
- 3Sketching Rational FunctionsA repeatable seven-step procedure: restrictions, intercepts, asymptotes, sign analysis around every critical value, behaviour near a hole, and then the sketch.Interactive9 questions
- 4Rational Equations and InequalitiesClear the denominators to solve an equation, then reject any root that was restricted. For inequalities, never multiply by a variable expression — collect on one side and use a sign chart that includes the undefined points.10 questions