Unit 1: Polynomial & Rational Functions
Precalculus · Unit 1 · Paper 3

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 37 terms and is the same for everyone, so a teacher can assign “Unit 1, Paper 3” 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 35 min 32 points0/17 attempted
1

Fundamental Theorem of Algebra

2

Piecewise function

3

Modeling with polynomial regression

4

Absolute value as a piecewise function

5

Concavity and points of inflection

6

Extrema and intervals

7

Zeros, roots, x-intercepts and solutions

8

Rational function domain

9

Complex conjugate pairs

10

Even and odd functions

11

Slant asymptote

12

Sign chart

Short answer 1. Define or explain: Increasing vs decreasing rate of change

3 pts

Short answer 2. Define or explain: Turning points

3 pts

Short answer 3. Define or explain: Rational Root Theorem

3 pts

Short answer 4. Define or explain: Solving absolute value inequalities

3 pts

Free response

8 pts

The rational function f is given by f(x) = (2x² − 8)/(x² − x − 6). (a) Find all zeros of f and all values of x where f is undefined, and classify each undefined point as a hole or a vertical asymptote. (b) Determine the horizontal asymptote of the graph of f, and justify your answer using end behavior. (c) Write the coordinates of the hole in the graph of f.