Unit 1 Practice Test: Polynomial and Rational Functions
Take the AP Precalculus Unit 1 practice test covering polynomial and rational functions, asymptotes, zeros, and transformations. Sharpen your skills before exam day.
What Unit 1 Covers
Unit 1 of AP Precalculus builds the foundation for all function reasoning that follows. It focuses on polynomial and rational functions, requiring students to analyze behavior, identify key features, and connect algebraic and graphical representations.
Core Topics in Unit 1
- Polynomial function behavior: degree, leading coefficient, end behavior
- Zeros of polynomials: multiplicity, x-intercepts, and graph behavior at each zero
- Rational functions: domain restrictions, vertical and horizontal asymptotes, holes
- Piecewise-defined functions and their graphs
- Function transformations: translations, reflections, dilations
- Average rate of change and function notation
Key AP Skills Tested in Unit 1
The AP exam emphasizes conceptual understanding alongside procedural fluency. In Unit 1, students are expected to:
- Determine end behavior and local behavior of polynomials from equations and graphs
- Identify removable and non-removable discontinuities in rational functions
- Describe transformations precisely using function notation
- Connect multiple representations: graph, table, equation
Common Mistakes to Avoid
Students frequently lose points in Unit 1 by making these errors:
- Confusing a hole with a vertical asymptote when a factor cancels
- Misidentifying end behavior when the leading coefficient is negative
- Forgetting to account for even versus odd multiplicity at a zero when sketching graphs
- Applying transformations in the wrong order
How to Use This Unit Test
Attempt the Unit 1 test after completing your initial study of polynomial and rational functions. Review every question you answered incorrectly and identify whether the error was conceptual or computational. Retake the test after targeted review to confirm improvement before moving to Unit 2 material.