Range

Definition

The range of a function is the set of all possible output values or the set of all values that the function can attain. It represents the complete set of values that a function can produce given its domain.

5 Must Know Facts For Your Next Test

1. The range of a function is the set of all possible output values, while the domain is the set of all possible input values.
2. The range of a function can be determined by analyzing the behavior of the function, such as its maximum and minimum values, asymptotes, and any restrictions on the output.
3. Limits and continuity are closely related to the range of a function, as they help determine the behavior of the function and the values it can attain.
4. Identifying the range of a function is important in understanding the function's behavior and its applications in various fields, such as optimization problems and graphical analysis.
5. The range of a function can be affected by transformations, such as translations, reflections, and scalings, which can change the set of output values the function can produce.

Review Questions

• Explain the relationship between the domain and range of a function.
  • The domain and range of a function are closely related concepts. The domain represents the set of all possible input values for the function, while the range represents the set of all possible output values. The range of a function is directly determined by the function's domain and the way the function maps the input values to the output values. Understanding the relationship between the domain and range is crucial in analyzing the behavior and properties of a function.
• Describe how limits and continuity affect the range of a function.
  • Limits and continuity are important factors in determining the range of a function. The limit of a function at a point represents the value that the function approaches as the input approaches that point. Continuity, on the other hand, ensures that the function has a well-defined value at a point and that the function's behavior is smooth and predictable. Both limits and continuity play a role in shaping the range of a function, as they help identify the values that the function can attain and the restrictions on the output values.
• Analyze how transformations can affect the range of a function.
  • Transformations, such as translations, reflections, and scalings, can significantly impact the range of a function. These transformations can change the set of output values that the function can produce, either by shifting the function's graph, reflecting it, or stretching or compressing it. Understanding how different transformations affect the range of a function is crucial in graphical analysis, optimization problems, and other applications where the range of a function is an important consideration.

Related terms

Domain: The domain of a function is the set of all possible input values for which the function is defined.

Limit: The limit of a function at a point is the value that the function approaches as the input approaches that point.

Continuity: A function is continuous at a point if it has a limit at that point and the limit is equal to the function's value at that point.