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 37 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 36 min 33 points0/17 attempted
1

Zeros, roots, x-intercepts and solutions

2

Increasing vs decreasing rate of change

3

Slant asymptote

4

Hole vs vertical asymptote

5

Remainder Theorem

6

Sign chart

7

End behavior of a rational function

8

Describing function behavior in words

9

Horizontal asymptote rules

10

Extrema and intervals

11

Symmetry of a rational function

12

Degree and end behavior

Short answer 1. Define or explain: Average rate of change

3 pts

Short answer 2. Define or explain: Solving polynomial inequalities

3 pts

Short answer 3. Define or explain: Absolute value as a piecewise function

3 pts

Short answer 4. Define or explain: Inverse function

3 pts

Free response

9 pts

Let f(x) = (2x² − 8)/(x² − x − 6).

Determine the domain of f, and identify each excluded value as a hole or a vertical asymptote with justification.

Determine the horizontal asymptote of f and justify your answer using end behavior.

Determine all x-intercepts of f.

Describe the behavior of f as x approaches each vertical asymptote from both sides.