Interval notation for domain and range is a concise way to describe every allowable input and every possible output of a function. By mastering parentheses, brackets, union symbols, and infinity, readers can express mathematical sets clearly and solve problems involving functions more efficiently Simple as that..
Introduction
A function connects each input value, usually written as x, with an output value, usually written as y. Two important sets describe a function:
- The domain is the set of all valid input values.
- The range is the set of all resulting output values.
Take this: if a function is defined as $f(x)=x^2+1$, every real number can be used as an input. Its domain is therefore all real numbers. Because a square is never negative, the smallest output occurs when $x=0$. Now, the output is then $1$, and every value greater than $1$ can also be produced. The range is $[1,\infty)$.
Interval notation provides a compact way to write these sets. Instead of saying “all numbers greater than or equal to 1 and less than infinity,” we can write $[1,\infty)$.
Introduction to Interval Notation
Interval notation represents a continuous set of numbers between two endpoints. The symbols at the endpoints show whether those values are included.
| Notation | Meaning | Example |
|---|---|---|
| $(a,b)$ | $a<x<b$ | $(2,8)$ means numbers greater than 2 and less than 8 |
| $[a |
