Domain and Range Study Guide

What is Domain and Range?

Domain: The domain of a function is the set of all possible input values (x-values) for which the function is defined. It is the set of all x-values for which the function is meaningful.

Range: The range of a function is the set of all possible output values (y-values) that the function can produce based on its input values. It is the set of all y-values that the function can produce.

Finding the Domain and Range

To find the domain of a function, look for any restrictions on the input values. This may include restrictions on the denominator of a fraction, restrictions on the square root of a number, or restrictions on the values inside a logarithm or trigonometric function.

To find the range of a function, consider the output values that the function can produce based on the input values. This may involve analyzing the behavior of the function, finding the maximum and minimum values, and determining any restrictions on the output values.

Examples

Example 1: Find the domain and range of the function f(x) = x^2.

Solution: The domain of f(x) = x^2 is all real numbers because there are no restrictions on the input values. The range of f(x) = x^2 is all non-negative real numbers (i.e., y ≥ 0) because the function always produces non-negative output values.

Example 2: Find the domain and range of the function g(x) = 1/x.

Solution: The domain of g(x) = 1/x is all real numbers except x = 0 because the function is undefined at x = 0. The range of g(x) = 1/x is all real numbers except y = 0 because the function never produces an output of 0.

Summary

In summary, the domain of a function represents all the possible input values for which the function is defined, while the range represents all the possible output values that the function can produce based on its input values.

◂Math Worksheets and Study Guides Eighth Grade. Real numbers

The resources above cover the following skills:

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8-NS1]

Expressions and Equations

Work with radicals and integer exponents.

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. [8-EE2]