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Functions and Readiness Checkpoint

A free Algebra II lesson from the “Functions and Notation” unit, with a worked example and practice problems including step-by-step solutions.

This checkpoint reviews Algebra II readiness skills around function notation, domain and range, transformations, inverses, and composition.

What you'll learn

Why it matters: This checkpoint rehearses everything in the Functions unit: notation, domain, range, inverses, composition, and transformations. Every later Algebra II topic — quadratics, polynomials, exponentials, logs — treats these as the assumed vocabulary.

Worked example

Problem. If f(x) = 2x + 3 and g(x) = x - 5, find f(g(9)).

  1. Evaluate inside first: g(9) = 4.
  2. Now find f(4).
  3. 2(4) + 3 = 11.

Answer: 11

Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. If f(x) = 4x - 1, find f(6).

Show solution
  1. 4(6) - 1 = 23.

Answer: 23

2. For points (1, 4), (2, 6), and (3, 6), the range is...

Choices: {4, 6} · {1, 2, 3} · {1, 4} · {2, 3, 6}

Show solution
  1. Range uses output values.

Answer: {4, 6}

3. For f(x) = 1/(x - 8), what value is excluded?

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  1. The denominator cannot be zero.

Answer: 8

4. y = f(x + 2) shifts the graph...

Choices: Left 2 · Right 2 · Up 2 · Down 2

Show solution
  1. Inside changes feel backward.

Answer: Left 2

5. If f(x) = x + 12, find f^-1(20).

Show solution
  1. Undo adding 12.

Answer: 8

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