Function Notation f(x) — SAT Math Explained
A way of writing functions that explicitly names the function and its input variable: f(x) is read 'f of x' and represents the output of function f when the input is x.
The Core Idea
Function notation is precise and powerful — it lets you reference specific outputs, evaluate at multiple inputs simultaneously, compose functions, and communicate mathematical ideas clearly.
Key Vocabulary
The output of function f at input x
The output when x = 3 — substitute 3 for x in the function rule
A rule assigning exactly one output to each input
Substituting a specific value for x to find the output
Using the output of g as the input for f
Evaluation Process
To find f(a): substitute a everywhere x appears in the function rule
f(x) = 3x² - 2, find f(4): f(4) = 3(4)² - 2 = 3(16) - 2 = 48 - 2 = 46
Interpreting
The y-intercept is 5
x = 3 is a zero/root of the function
Two different inputs give the same output — the function takes the same value at a and b
Multiple Input Types
Numeric: f(3) — substitute 3
Algebraic: f(x + 1) — substitute x + 1 everywhere x appears and simplify
Variable: f(a) — substitute a
Common Errors to Avoid
Reading f(x) as 'f times x' — it's not multiplication, it's function notation
Not substituting the input everywhere the variable appears
Confusing f(x+1) with f(x) + 1 — these are different things
Practice: Function Notation f(x)
5 SAT-style questions. Select your answer and get an instant explanation.
If f(x) = 2x + 3, what is f(4)?
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