MathIsimple

Functions & Function Notation

Learn what functions are, how to use function notation, and how to determine if a relationship is a function.

8th Grade
Algebra
~45 min
🎮 Interactive Activity: Function Machine

Put a number in, get a number out! Functions are like machines.

Input (x)
3
Function: f(x) = 2x + 1
f(x)
Output
?
f(3) = ?
🎮 Interactive Activity: Vertical Line Test

Test if a relation is a function using the vertical line test!

1. What is a Function?

📚 Function Definition

A function is a special type of relation where each input (x-value) has exactly one output (y-value).

Key Rule: For every x, there is exactly one y

Input
x
→
Function
f
→
Output
y
✓ Is a Function

{ (1,2), (2,4), (3,6), (4,8) }
Each x has one y

✗ Not a Function

{ (1,2), (1,3), (2,4) }
x=1 has two y-values

2. Function Notation
3. Domain and Range
4. Vertical Line Test
5. Types of Functions
6. Real-World Applications
7. Worked Examples
8. Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What is a function?
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2
If f(x) = 2x + 3, what is f(5)?
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3
Which relation is NOT a function?
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4
What is the domain of the function f(x) = 1/(x-2)?
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5
If g(x) = x² - 4, what is g(-3)?
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6
What does the vertical line test determine?
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7
If f(x) = 3x - 1 and f(a) = 8, what is a?
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8
What is the range of f(x) = x²?
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9
Which notation represents 'f of x'?
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10
If h(x) = 5x + 2, what is the value of x when h(x) = 17?
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