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Polynomial and Rational Functions — High School Pre-Calculus practice questions

16 multiple-choice questions and 15 flashcards on Polynomial and Rational Functions, about 11% of the High School Pre-Calculus bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-02 · how we write and review questions

What this chapter covers

Polynomial and Rational Functions is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 16 of the bank's 150 multiple-choice questions — roughly 11% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Polynomial and Rational Functions practice questions

1 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

How many distinct real zeros does f(x) = x³ − 4x² + 4x have?

  1. 2
  2. 3
  3. 1
  4. 0

Answer: A — 2

A) Correct — f(x) = x(x − 2)², with zeros 0 and 2 (2 repeated). B) Counts the repeated zero twice; the question asks for distinct zeros. C) Misses the zero at x = 0. D) Misses both zeros.

Polynomial and Rational Functions flashcards

4 cards from the 15 in this chapter.

What is i, and what is i²?

i = √−1; i² = −1.

What is a hole in a rational function?

A point (a, b) removed from the graph because (x − a) cancels in numerator and denominator.

What is a slant (oblique) asymptote?

Occurs when degree of numerator = degree of denominator + 1; found by polynomial long division.

What is a horizontal asymptote? How do you find it?

A horizontal line y = L the function approaches as x → ±∞. Compare degrees of numerator and denominator: if deg(num) < deg(den), y = 0; equal, y = ratio of leading coefficients; greater, no horizontal asymptote.

Practise the full chapter

These are a sample. The full Polynomial and Rational Functions chapter runs 31 items with per-chapter progress tracking, on the web and in the iOS app.

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