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 SAT Practice 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

Evaluate f(x) for a given input
Interpret function notation in word problems
Find an input when the output is given
Compare values from tables, graphs, and equations

Dolphin question bank

Practice your skill

Question 1 of 3Easy

The function f is defined by f(x) = 80 - 6x. What is the value of f(7)?

Show answer and solution

Correct answerB. 38

Solution walkthrough

It's given that function $f$ is defined by $f (x) = 80 - 6 x$ .
The value of $f (7)$ can be found by substituting $7$ for $x$ in the given function, which yields $f (7) = 80 - 6 \times 7$ , or $f (7) = 80 - 42$ , which is equivalent to $f (7) = 38$ .
Therefore, the value of $f (7)$ is $38$ .

Why the other choices miss

Choice A is incorrect. This is the value of

80 - 67

, not

80 - 6 \times 7

. Choice C is incorrect. This is the value of

80 - 61

, not

80 - 6 \times 7

. Choice D is incorrect. This is the value of

80 - 6 + 7

, not

80 - 6 \times 7

Question 2 of 3Medium

If f(x) = x + 7 and g(x) = 7x, what is the value of 4f(2) - g(2)?

-5
1
22
28

Show answer and solution

Correct answerC. 22

Solution walkthrough

The value of $f (2)$ can be found by substituting $2$ for $x$ in the given equation $f (x) = x + 7$ , which yields $f (2) = 2 + 7$ , or $f (2) = 9$ .
The value of $g (2)$ can be found by substituting $2$ for $x$ in the given equation $g (x) = 7 x$ , which yields $g (2) = 7 (2)$ , or $g (2) = 14$ .
The value of the expression $4 f (2) - g (2)$ can be found by substituting the corresponding values into the expression, which gives $4 (9) - 14$ .
This expression is equivalent to $36 - 14$ , or $22$ .

Question 3 of 3Medium

The height, in feet, of an object x seconds after it is thrown straight up in the air can be modeled by the function h(x) = -16x^2 + 20x + 5. Based on the model, which of the following statements best interprets the equation h(1.4) = 1.64?

The height of the object 1.4 seconds after being thrown straight up in the air is 1.64 feet.
The height of the object 1.64 seconds after being thrown straight up in the air is 1.4 feet.
The height of the object 1.64 seconds after being thrown straight up in the air is approximately 1.4 times as great as its initial height.
The speed of the object 1.4 seconds after being thrown straight up in the air is approximately 1.64 feet per second.

Show answer and solution

Correct answerA. The height of the object 1.4 seconds after being thrown straight up in the air is 1.64 feet.

Solution walkthrough

The value 1.4 is the value of $x$ , which represents the number of seconds after the object was thrown straight up in the air.
When the function $h$ is evaluated for $x = 1.4$ , the function has a value of 1.64, which is the height, in feet, of the object.

Why the other choices miss

Choices B and C are incorrect and may result from misidentifying seconds as feet and feet as seconds. Additionally, choice C may result from incorrectly including the initial height of the object as the input

x

. Choice D is incorrect and may result from misidentifying height as speed.

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

Identify the requested input and the expression that defines the function.
Replace every variable with the input using parentheses.
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.