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Function Notation Review

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

Function notation names a rule. In f(x), x is the input and f(x) is the output. To evaluate a function, substitute the input everywhere the variable appears.

What you'll learn

Why it matters: Tax brackets, shipping rate tables, and fuel-economy charts use function notation so that the rule and the value are unambiguous. Reading f(7) as 'the output when the input is 7' keeps a calculation honest no matter how complex the rule is.

Worked example

Problem. If f(x) = 3x - 4, find f(7).

  1. Substitute 7 for x.
  2. f(7) = 3(7) - 4.
  3. 21 - 4 = 17.

Answer: 17

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 f(x) = 2x + 5, find f(3).

Show solution
  1. Substitute 3.
  2. 2(3) + 5 = 11.

Answer: 11

2. If g(x) = x^2 - 4, find g(6).

Show solution
  1. 6^2 - 4 = 32.

Answer: 32

3. If h(t) = 3t - 1, find h(-2).

Show solution
  1. 3(-2) - 1 = -7.

Answer: -7

4. In f(4) = 9, the output is...

Choices: 9 · 4 · f · 13

Show solution
  1. The function value is the output.

Answer: 9

5. If p(x) = x^2 + 2x and p(a) = 15 when a = 3, what is p(3)?

Show solution
  1. The notation p(a) means evaluate the rule at a.

Answer: 15

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