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 1 Paper 2 Paper 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 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 33 min 30 points0/17 attempted

Function notation and evaluation

Synthetic division

Hole vs vertical asymptote

Degree from a finite difference table

Endpoint inclusion in an inequality solution

Why a degree-n polynomial has at most n − 1 turns

End-behavior model of a rational function

Secant line vs tangent line

Reading multiplicity from a graph

Even and odd functions

Turning points

Placeholder coefficients in synthetic division

Short answer 1. Define or explain: Vertical asymptote is never crossed

3 pts

Short answer 2. Define or explain: Horizontal line test

3 pts

Short answer 3. Define or explain: Parity of a sum

3 pts

Short answer 4. Define or explain: Crossing a horizontal asymptote

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.