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Functions and Function Notation
A function assigns exactly one output to every allowed input; f(a) means substitute a for the input.
How it works
A function assigns exactly one output to every allowed input; f(a) means substitute a for the input. Name the quantities before calculating, keep each transformation logically equivalent, and check the result against the original conditions.
Worked example
If f(x)=3x−2, find f(5).
- Replace x with 5.
- Compute 3×5−2.
- 15−2=13.
f(5)=13.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Using a remembered formula without identifying what each symbol represents.
- Changing a value or condition during an intermediate step.
- Skipping the final substitution, estimate, or logical check.
Challenge
Find an input whose output is 25 for f(x)=4x+1.
Questions learners ask
What is the key idea in functions and function notation?
A function assigns exactly one output to every allowed input; f(a) means substitute a for the input.
How should I check an answer?
Substitute it into the original conditions, check units and signs, and decide whether its size is reasonable.