Range

Definition

The range of a set of data or a function is the difference between the largest and smallest values in the set. It represents the spread or variation within the data and is a measure of the dispersion or variability of the values.

5 Must Know Facts For Your Next Test

1. The range of a function is the set of all possible output values that the function can produce.
2. The range of an absolute value inequality is the set of all real numbers that satisfy the inequality.
3. The range of a rational function is determined by the behavior of the function as the input approaches the vertical asymptotes.
4. The range of a radical function is affected by the domain restrictions and the behavior of the function near the points where the radicand is zero.
5. The range of a quadratic function can be determined by the vertex and the direction of the parabola.

Review Questions

• Explain how the range of a function is related to the domain and codomain of the function.
  • The range of a function is the set of all possible output values that the function can produce, and it is a subset of the function's codomain. The domain of the function, which is the set of all possible input values, determines the range of the function. The relationship between the domain, range, and codomain is important in understanding the behavior and properties of a function.
• Describe how the range of an absolute value inequality is determined and how it differs from the range of a typical function.
  • The range of an absolute value inequality is the set of all real numbers that satisfy the inequality. Unlike the range of a typical function, which is determined by the behavior of the function over its domain, the range of an absolute value inequality is determined by the solution set of the inequality. The range of an absolute value inequality is often an interval, but it can also be the union of two intervals or the entire real number line, depending on the specific inequality.
• Analyze how the range of a rational function is affected by the presence of vertical asymptotes and the behavior of the function near these asymptotes.
  • The range of a rational function is determined by the behavior of the function as the input approaches the vertical asymptotes. As the input approaches a vertical asymptote, the output of the function approaches positive or negative infinity, depending on the behavior of the function. The range of a rational function is typically an interval or the union of two intervals, and it is often affected by the location and number of vertical asymptotes in the function's graph.

Related terms

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

Codomain: The codomain of a function is the set of all possible output values that the function can produce.

Interval: An interval is a set of real numbers that includes all the numbers between two given values, including or excluding the endpoints.