Domain and range

Definition

The domain of a function is the set of all possible input values (typically x-values) for which the function is defined. The range of a function is the set of all possible output values (typically y-values) that the function can produce.

5 Must Know Facts For Your Next Test

1. The domain can be found by identifying all x-values for which the function equation makes sense (e.g., excluding values that cause division by zero or negative square roots).
2. The range is determined by evaluating the function over its domain and finding all resulting y-values.
3. For polynomial functions, the domain is always all real numbers ($\mathbb{R}$).
4. In rational functions, any value that makes the denominator zero should be excluded from the domain.
5. For functions involving square roots, ensure that the expression inside the root is non-negative to determine the domain.

Review Questions

• How do you determine the domain of a rational function?
• What steps are involved in finding the range of a given function?
• Why are certain x-values excluded from a function's domain?

Related terms

Function: A relation where each input has exactly one output.

Inverse Function: A function that reverses another function, swapping its domain and range.

$\mathbb{R}$ (Real Numbers): The set of all rational and irrational numbers, representing continuous values on a number line.