Integrated Math 1 / Unit 3: Functions
3.3 Domain and Range
Notes
The domain is the set of all allowed inputs. The range is the set of all resulting outputs.
- From ordered pairs, domain = list of $x$-values; range = list of $y$-values (list repeats once).
- In a real situation, the domain must make sense: you cannot have negative people or a fraction of a ticket.
- Example: $f(x) = 2x + 1$ with domain $\{0, 1, 2, 3\}$ has range $\{1, 3, 5, 7\}$.
- Discrete data has separate points; continuous data includes all values between.
Practice
What is the domain of $\{(-2, 5), (0, 3), (1, 5), (4, -1)\}$?
The domain is the set of all $x$-values.
The function $f(x) = 2x + 1$ has domain $\{0, 1, 2, 3\}$. What is its range?
$f(0) = 1$, $f(1) = 3$, $f(2) = 5$, $f(3) = 7$.
A bus holds at most 40 riders and each rider pays $2. For the function $C(n) = 2n$, what is the best domain?
The number of riders $n$ must be a whole number from 0 to 40.
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