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Functions Checkpoint

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

This checkpoint samples function notation, domain and range restrictions, composition, inverse functions, and transformation readiness.

What you'll learn

Why it matters: This checkpoint connects the language of functions to valid inputs, outputs, composition, and inverse reasoning. A parent or student can read it as evidence that function notation is becoming a usable tool, not just a symbol pattern.

Worked example

Problem. If f(x) = x + 2 and g(x) = 4x, find f(g(3)).

  1. g(3) = 12.
  2. f(12) = 14.
  3. So f(g(3)) = 14.

Answer: 14

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) = 2x - 5, find f(9).

Show solution
  1. 18 - 5 = 13.

Answer: 13

2. For h(x) = 1/(x - 10), what value is excluded?

Show solution
  1. x - 10 cannot be 0.

Answer: 10

3. If f(x) = x^2 and g(x) = x + 1, find f(g(4)).

Show solution
  1. g(4) = 5, then f(5) = 25.

Answer: 25

4. The inverse of f(x) = x + 6 is...

Choices: f^-1(x) = x - 6 · f^-1(x) = x + 6 · f^-1(x) = 6x · f^-1(x) = x/6

Show solution
  1. Undo adding 6.

Answer: f^-1(x) = x - 6

5. For h(x) = sqrt(2x - 6), what is the smallest allowed x-value?

Show solution
  1. 2x - 6 must be at least 0.

Answer: 3

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