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Functions and Their Graphs — High School Pre-Calculus practice questions

16 multiple-choice questions and 17 flashcards on Functions and Their Graphs, 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

Functions and Their Graphs 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 Functions and Their Graphs practice questions

2 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.

f(x) = x² and g(x) = x + 1. Find (f ∘ g)(2).

  1. 5
  2. 9
  3. 4
  4. 3

Answer: B — 9

B) Correct — (f ∘ g)(2) = f(g(2)) = f(3) = 9. A) Computes (g ∘ f)(2) = g(4), applying the functions in the wrong order. C) Finds f(2) and never applies g. D) Finds g(2) and never applies f.

y = −(x + 3)² + 2 is a transformation of y = x². Where is its vertex, and which way does it open?

  1. Vertex (3, 2), opening down
  2. Vertex (−3, 2), opening up
  3. Vertex (−3, −2), opening down
  4. Vertex (−3, 2), opening down

Answer: D — Vertex (−3, 2), opening down

D) Correct — Shift left 3, up 2, and reflect across the x-axis. A) Reads x + 3 as a shift to the right. B) Ignores the negative sign in front, which flips the parabola. C) Applies the reflection to the vertical shift as well.

Functions and Their Graphs flashcards

4 cards from the 17 in this chapter.

What is function composition (f∘g)(x)?

(f∘g)(x) = f(g(x)) — apply g first, then f.

What is the inverse of a function?

f⁻¹(x) reverses f(x) — swap x and y, then solve for y. Composition: f(f⁻¹(x)) = x.

What is the domain of f(x) = 1/(x − 2)?

All real numbers except x = 2: (−∞, 2) ∪ (2, ∞).

What is an even function? Give a graphical property.

f(−x) = f(x). Symmetric about the y-axis. Example: x², cos x.

Practise the full chapter

These are a sample. The full Functions and Their Graphs chapter runs 33 items with per-chapter progress tracking, on the web and in the iOS app.

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