# 2.7 Review and Summary

## Additional Resources

Access these online video resources for additional instruction and practice with domain and range.

## Key Terms

**Interval Notation** – a method of describing a set that includes all numbers between a lower limit and an upper limit; the lower and upper values are listed between brackets or parentheses, a square bracket indicating inclusion in the set, and a parenthesis indicating exclusion

**Piecewise Function** – a function in which more than one formula is used to define the output

**Set-builder Notation** – a method of describing a set by a rule that all of its members obey; it takes the form [latex]\{x\vert statement\;about\}\;x[/latex]

## Key Concepts

- The domain of a function includes all real input values that would not cause us to attempt an undefined mathematical operation, such as dividing by zero or taking the square root of a negative number.
- The domain of a function can be determined by listing the input values of a set of ordered pairs. See 2.2 Finding the Domain of a Function Defined by an Equation.
- The domain of a function can also be determined by identifying the input values of a function written as an equation. See 2.2 Finding the Domain of a Function Defined by an Equation.
- Interval values represented on a number line can be described using inequality notation, set-builder notation, and interval notation. See 2.3 Using Notations to Specify Domain and Range.
- For many functions, the domain and range can be determined from a graph. See 2.4 Finding Domain and Range from Graphs.
- An understanding of toolkit functions can be used to find the domain and range of related functions. See 2.5 Finding Domains and Ranges of the Toolkit Functions.
- A piecewise function is described by more than one formula. See 2.6 Graphing Piecewise-Defined Functions.
- A piecewise function can be graphed using each algebraic formula on its assigned subdomain. See 2.6 Graphing Piecewise-Defined Functions.

Access for free at https://openstax.org/books/precalculus/pages/1-introduction-to-functions