📖Definition
A function is a special relationship between inputs and outputs where each input has exactly one output. Think of it as a machine: you put in a number (input), and the function gives you back exactly one result (output). Functions are written as f(x).
📐Formula
In f(x) = 2x + 3: f is the function name, x is the input, and 2x + 3 tells you how to calculate the output. f(4) means "substitute 4 for x": f(4) = 2(4) + 3 = 11.
📝Step-by-Step Guide
Understanding Function Notation
f(x) is read "f of x." The letter in parentheses is the input variable.
Evaluating Functions
To find f(a), replace every x in the function rule with a.
Identify Domain and Range
Domain is all possible inputs; range is all possible outputs.
Use the Vertical Line Test
A graph represents a function if any vertical line crosses it at most once.
⚠️Common Mistakes to Avoid
- Thinking f(x) means f times x
- Confusing function notation with multiplication
- Forgetting that each input can only have one output
- Not substituting correctly when evaluating
- Confusing domain (inputs) with range (outputs)
✏️Practice Problems
If f(x) = x + 7, find f(3)
Answer: 10
If g(x) = x² - 4x, find g(-2)
Answer: 12
If f(x) = 2x + 1, find x when f(x) = 15
Answer: x = 7
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