Domain

Definition

The domain of a function is the set of all possible input values (typically $x$-values) for which the function is defined. It represents all the values that can be plugged into the function without causing any undefined behavior.

5 Must Know Facts For Your Next Test

1. If a function includes a fraction, the denominator cannot be zero as division by zero is undefined.
2. For functions involving square roots or other even-numbered roots, the radicand must be greater than or equal to zero to produce real numbers.
3. Polynomial functions have domains that are all real numbers since they are defined for every $x$ value.
4. When determining the domain of a composite function, consider both the inner and outer functions' domains.
5. Logarithmic functions require their arguments to be positive, as logarithms of non-positive numbers are undefined in real numbers.

Review Questions

• What is the domain of $f(x) = \frac{1}{x-2}$?
• Determine the domain of $g(x) = \sqrt{x+3}$.
• How do you find the domain of a composite function $h(x) = f(g(x))$?

Related terms

Range:

The set of all possible output values (typically $y$-values) that a function can produce.

Composite Function: A function created by applying one function to the results of another, denoted as $(f \circ g)(x) = f(g(x))$.

Asymptote: A line that a graph approaches but never touches or crosses.