Functions and Graphs
Domain and Range – The Inputs and Outputs of a Function
The domain of a function is the complete set of values it's allowed to take as inputs, and the range is the complete set of values it can produce as outputs. If you think of a function as a machine, the domain is everything you're allowed to feed in, and the range is everything that can possibly come out the other end.
Domain and range aren't just abstract vocabulary – they matter because not every input makes sense for every function (you can't divide by zero, for instance), and knowing a function's range tells you immediately what kind of outputs to expect, without having to test every single input first.
Domain vs. Range
Domain = the set of possible inputs (x-values). Range = the set of possible outputs (y-values).
y = 3(3) − 1 = 9 − 1 = 8.
Real-Life Application
- Age restrictions: a ride's height requirement defines a domain of allowed inputs.
- Thermostats: a heater's possible output temperatures form its range.
- Grading systems: a percentage score's possible range is limited to 0-100.
Key Takeaways
- The domain is a function's set of possible inputs.
- The range is a function's set of possible outputs.
- Not every value makes sense as an input for every function.