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SAT Math skill page

SAT Function Notation Practice

Read f(x) as a rule: plug in the input carefully, then answer what the output means.

Practice function notation in Dolphin SATPractice questions
10-16 min practice time3 questions on pageAdvanced Math
Practice time10-16 min
Question bank3 questions
Best forAdvanced Math

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
If f(x) = 2x + 7, what is f(4)?
  1. 8
  2. 11
  3. 15
  4. 22
Show answer and solution
Correct answerC. 15

Solution walkthrough

  1. Substitute 4 for x: f(4) = 2(4) + 7 = 15.
Question 2 of 3Medium
If g(x) = - 3 and g(a) = 13, which could be the value of a?
  1. -4
  2. -3
  3. 3
  4. 13
Show answer and solution
Correct answerA. -4

Solution walkthrough

  2. The possible values are 4 and -4.
Question 3 of 3Hard
A function h gives the total cost, in dollars, of buying n tickets. What does h(6) = 84 mean?
  1. Six tickets cost $84.
  2. Eighty-four tickets cost $6.
  3. Each ticket costs $84.
  4. The function has 6 outputs.
Show answer and solution
Correct answerA. Six tickets cost $84.

Solution walkthrough

  1. The input is the number of tickets and the output is total cost, so h(6) = 84 means 6 tickets cost $84.

Avoid these traps

Common mistakes on this skill

Reading f(x) as multiplication

Function notation names the output produced by input x; it does not mean f times x.

Substituting into only one occurrence of the variable

The input must replace every occurrence of the function variable, with parentheses when needed.

Study plan

How to practice this skill in Dolphin

  1. Identify the requested input and the expression that defines the function.
  2. Replace every variable with the input using parentheses.
  3. Simplify in order and interpret the output in the context of the question.
Practice function notation in Dolphin SAT

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FAQ

Questions about SAT Function Notation Practice

What does f(3) mean?

It is the output of function f when the input is 3.

Is f(x) the same as y?

Both can represent the output of a function; f(x) additionally identifies the function and its input.