Precalculus · Grades 10 to 12
Functions and domains
Find the inputs that a function allows.
The idea
A function pairs each input with exactly one output. Its domain is the set of inputs that give a real output.
Two numbers are forbidden: a denominator of zero and a square root of a negative number. Check for both when you find a domain.
Worked examples
- How to Find the Domain of a Function Find the domain of f(x) = 1/(x - 4). Three steps, the zero-denominator rule, and the set-notation mistakes to avoid.
- How to Evaluate a Logarithm Evaluate log base 2 of 32. Three steps, the power question, and the base-and-answer mix-up to avoid.
- How to Solve an Exponential Equation Solve 3^x = 81 by writing both sides as powers of 3. Three steps, the matching-base reason, and the log mistakes to avoid.
Practice this topic
4 problems with answers.