Functions
Domain, range, and function notation
lessons (2)
Domain and Range
Learn how to identify the domain (input values) and range (output values) of a function.
Function Notation f(x)
Learn to read and use function notation to describe mathematical relationships.
Functions describe relationships where each input has exactly one output. Understanding function notation, domain, range, and behavior is fundamental to higher mathematics. Functions model real-world relationships from distance-time to cost-quantity to population-time.
What Students Will Learn
- Identify functions from graphs, tables, and equations
- Use function notation f(x)
- Determine domain and range
- Evaluate functions at given values
- Graph functions by plotting points
Frequently Asked Questions
What makes something a function?
Each input (x-value) produces exactly one output (y-value). The vertical line test checks this: if any vertical line crosses the graph more than once, it is not a function.
What is the difference between domain and range?
Domain is all possible input values (x). Range is all possible output values (y). Domain is where you start; range is where you can end up.
What does f(3) mean?
It means evaluate the function f at x = 3. If f(x) = 2x + 1, then f(3) = 2(3) + 1 = 7.