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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
D. Characteristics of Functions
60. 12AF.D3.1
60.1 Function notation (advanced)
Function Notation
Function notation writes a function as f(x), where f names the function, x is the input, and f(x) is the output.
What You'll Learn
f(x) is read 'f of x', not 'f times x' f names the function, x is the input.
The whole expression f(x) represents the output value.
To evaluate f(x) at a number, substitute that number for every x in the rule.
Function notation lets you name multiple functions clearly, like f(x), g(x), h(x).
f(x) + 2 shifts a graph up; f(x + 2) shifts it left the notation encodes the transformation.
What You'll Practice
1
Substituting numbers, variables, and expressions into polynomial functions
2
Rewriting square root expressions using function notation
3
Reading function values and coordinates from graphs
4
Finding x-values that produce specific function outputs
Why This Matters
Function notation is the language of advanced mathematics. You'll use f(x) notation in every math course from algebra through calculus, and it's essential for understanding how variables relate in science, engineering, and data analysis.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Learning resources
Skills
Function Notation
Substitution
Graphing Functions
Function Evaluation
Algebraic Expressions
Coordinate Interpretation
ON Curriculum Aligned