Function Notation
f(x) names a function and shows its input.
About this topic
Function notation writes a function as f(x), read "f of x". The letter f names the rule and x is the input, so f(3) means "the output when x is 3". If f(x) = 2x + 1, then f(3) = 7. It does not mean f multiplied by x.
The notation makes it easy to talk about many functions at once, using different letters such as g(x) or h(t), and to compare their values: f(3) versus g(3). You can also substitute expressions, so f(a + 1) = 2(a + 1) + 1 = 2a + 3. Evaluating at a graph means reading the height of the curve above x.
In science, you might write d(t) for distance after t seconds or C(n) for the cost of n items, which tells the reader exactly what the variables stand for. Spreadsheet formulas and programming languages use the same idea of naming a rule and feeding it inputs.
The most common mistake is to distribute as if f were a number: f(x + 2) is not f(x) + f(2). Substitute the entire expression in place of x, using parentheses to protect negatives. For example, if f(x) = x², then f(−3) = (−3)² = 9.
Key ideas
- f(3) means substitute 3
- The letter can be anything
- f(x) is read f of x
Quick check
Use cases: where Function Notation helps
- Homework: review the key idea behind Function Notation before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Function Notation without notes.
- Visual learning: play with the interactive lab to see how Function Notation changes when you adjust its inputs.
- Teaching a friend: explain Function Notation in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Function Notation?
f(x) names a function and shows its input.
What will I learn in Function Notation?
f(3) means substitute 3. The letter can be anything. f(x) is read f of x.
Is Function Notation part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Function Notation lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Function Notation?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.