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Function Notation

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

Function notation names a rule. If f(x) = 2x + 3, then f(4) means use 4 as the input. The output is found by substituting the input into the expression.

What you'll learn

Why it matters: Calculators, spreadsheets, tax tables, and science formulas all use function notation to show which input is being used. Reading f(5) as the output for input 5 helps prevent the common mistake of treating notation like multiplication.

Worked example

Problem. If f(x) = 3x - 5, find f(6).

  1. Replace x with 6.
  2. Compute 3(6) - 5.
  3. 18 - 5 = 13.

Answer: 13

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. If g(x) = x^2 + 1, find g(5).

Show solution
  1. Replace x with 5.
  2. 5^2 + 1 = 25 + 1 = 26.

Answer: 26

2. If h(x) = 4x - 9, what does h(2) mean?

Choices: Multiply h by 2 · Use 2 as the input · Set h equal to 2 · Divide by 2

Show solution
  1. The number in parentheses is the input value.
  2. h(2) means evaluate h when x = 2.

Answer: Use 2 as the input

3. If p(x) = 2x^2 - 3, find p(4).

Show solution
  1. 2(16) - 3 = 29.

Answer: 29

4. If f(x) = x^2 - 2x, find f(5).

Show solution
  1. Substitute 5: 25 - 10 = 15.

Answer: 15

5. If f(3) = 12, then 12 is the...

Choices: Output when the input is 3 · Input when the output is 3 · Slope of f · Name of the function

Show solution
  1. The value in parentheses is the input.

Answer: Output when the input is 3

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