Function Notation
f(x) names the output for input x.
Key idea
f(x) names the output for input x.
In depth
f(x) names a function and its input. f(3) means substitute 3 for x. The notation helps you track many functions and evaluate them at specific inputs without confusion.
Worked example
If f(x) = x² + 1, then f(3) = 10 and f(a + 1) = (a+1)² + 1.
Formula
Real-world uses
- Writing formulas in spreadsheets and code, such as f(x) = 2x + 3, to compute outputs
Common mistake
Reading f(x) as f times x.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Function Notation?
f(x) names the output for input x. It is a topic at the intermediate level in Algebra.
What is the formula for Function Notation?
The key formula is f(3).
Where is Function Notation used in real life?
Real-world examples: Writing formulas in spreadsheets and code, such as f(x) = 2x + 3, to compute outputs.
What should I learn before Function Notation?
Make sure you are comfortable with Linear Functions, the previous topic in Algebra.
What is a common mistake with Function Notation?
Reading f(x) as f times x.
How can I practise Function Notation?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Function Notation?
Move on to Domain and Range next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.