Unit 1: Polynomial & Rational Functions
Precalculus · Unit 1 · Paper 1

Polynomial & Rational Functions unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 87 terms and is the same for everyone, so a teacher can assign “Unit 1, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 33 min 30 points0/17 attempted
1

Odd-degree real polynomial

2

Real quadratic from a conjugate pair

3

Even and odd functions

4

Parity of a product

5

Why you cannot multiply out a rational inequality

6

Constant term and parity

7

Solving polynomial inequalities

8

Synthetic division

9

Reducing a cubic with a known zero

10

Symmetry of a rational function

11

Decomposing a function

12

Zeros, roots, x-intercepts and solutions

Short answer 1. Define or explain: Turning points

3 pts

Short answer 2. Define or explain: Residual plot patterns

3 pts

Short answer 3. Define or explain: Rational function domain

3 pts

Short answer 4. Define or explain: Bounds on the number of real zeros

3 pts

Free response

6 pts

The function f is given by f(x) = (x³ − 4x² + x + 6)/(x − 3).

Show that x = 3 is a zero of the numerator, and use this to simplify f. State the domain of f and identify what occurs at x = 3.

Determine all x-intercepts of f.

Determine the end behavior of f, and explain why f has no horizontal or slant asymptote.

The numerator of f has three real zeros. Determine them, and explain why a cubic with real coefficients must have at least one real zero.