Function Notation and Evaluating Outputs

Algebra Foundation

Algebra 1

Study expressions, equations, inequalities, functions, linear models, systems, polynomials, quadratics, and exponential growth with original explanations and worked examples.

Learn with original explanations and worked examples. OpenStax Elementary Algebra 2e was consulted for topic coverage.

Study every current unit through original concept lessons, formula derivations, experiments, quizzes, and practice sets.

Algebra 1 · Unit 4 · Topic 4.2

Function Notation and Evaluating Outputs

The notation f(x) denotes the output of function f at input x, not multiplication of f and x.

Definition and explanation

The notation f(x) denotes the output of function f at input x, not multiplication of f and x. A formula can define a function on an explicitly specified domain.

Worked example

If f(x) = 3x − 8, then f(5) = 15 − 8 = 7 and f(a + 2) = 3(a + 2) − 8 = 3a − 2. Replace the entire input slot, using parentheses for expressions.

Common mistake

The expression f(a + 2) does not generally equal f(a) + 2.

Key takeaway

The notation f(x) denotes the output of function f at input x, not multiplication of f and x.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.