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Example: For f(x) = 2x + 3, enter m = 2
📌 Quick Examples — Click to Try
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📚 Common Functions — Domain & Range Reference
| Function Type | Example | Domain | Range |
|---|---|---|---|
| Linear | f(x) = 2x + 1 | All real numbers (−∞, ∞) | All real numbers (−∞, ∞) |
| Quadratic (a>0) | f(x) = x² | (−∞, ∞) | [0, ∞) |
| Quadratic (a<0) | f(x) = −x² | (−∞, ∞) | (−∞, 0] |
| Square Root | f(x) = √x | [0, ∞) | [0, ∞) |
| Rational | f(x) = 1/x | x ≠ 0 | y ≠ 0 |
| Absolute Value | f(x) = |x| | (−∞, ∞) | [0, ∞) |
| Cubic | f(x) = x³ | (−∞, ∞) | (−∞, ∞) |
What Are Domain and Range?
In math class, when you study a function like f(x) = 2x + 1, the domain is the set of all x-values (inputs) you are allowed to plug in, and the range is the set of all y-values (outputs) you can get out.
🔵 Domain — The Allowed Inputs
Think of the domain as a guest list for the function. Most functions let any real number in — those have domain "All Real Numbers," written as (−∞, ∞) in interval notation. But some functions have rules:
• Square root functions — you can't take the square root of a negative number, so x must be ≥ some value.
• Rational functions — the denominator can never be zero, so we exclude the x-value that makes it zero.
🟢 Range — The Possible Outputs
The range is every y-value the function is capable of producing. A basic quadratic f(x) = x² only produces zero or positive values, so its range is [0, ∞). A linear function can produce any output, so its range is (−∞, ∞).
📝 Interval Notation Explained
Interval notation is a compact way to write sets of numbers:
• Parenthesis ( ) — the endpoint is NOT included (open interval)
• Bracket [ ] — the endpoint IS included (closed interval)
• ∞ always uses a parenthesis because infinity is never actually reached.
🚀 Tips for US Students (Common Core & Pre-Calc)
Understanding domain and range is a foundational skill covered in 8th grade through Pre-Calculus. On standardized tests like the SAT and ACT, function questions often test whether you know which x-values a function accepts. Remember: look for square roots and denominators first — those are the two most common restrictions.