Exercises: Graph Rational Functions

Work through each section in order. Show your work where indicated. Factor all rational expressions completely before identifying key features.

Grade 9·20 problems·~30 min·Common Core Math - HS Functions·standard·hsf-if-c-7d

Work through problems with immediate feedback

Fluency Practice

Let $g(x) = \frac{x^2 - x - 6}{x^2 - 4}$ . After factoring and simplifying, which describes the key features?

Zero at $x = 3$ ; vertical asymptote at $x = 2$ ; hole at $x = -2$

Zeros at $x = 3$ and $x = -2$ ; vertical asymptotes at $x = 2$ and $x = -2$

Zero at $x = 3$ ; vertical asymptotes at $x = 2$ and $x = -2$ ; no holes

Zero at $x = -2$ ; vertical asymptote at $x = 3$ ; hole at $x = 2$