What is the Range of the Following Function? {(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}

In mathematics, understanding the range of a function is crucial for analyzing its output behavior based on various inputs. The range specifically pertains to all the possible values a function can yield when different inputs from its domain are applied. For instance, consider the function represented by the set of ordered pairs {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}. The objective is to determine the range associated with these pairs. This article aims to clarify the concept of the range, outline steps for its calculation, and provide useful explanatory examples. Whether you are new to the topic or seeking to deepen your comprehension, this guide will equip you with the necessary tools to identify the range of a function effectively.

The range of a function encompasses all possible output values (y-values) that the function can produce. In ordered pairs, each pair features an input (x-value) and its corresponding output (y-value). To determine the range for the given function, we need to extract the y-values from the pairs: for this function, they are 0, –3, –9, 5, and 7. When listed as a set, the range is expressed as {0, –3, –9, 5, 7}. Understanding the range is pivotal, as it reveals the potential outputs of the function based on its corresponding domain (x-values).

To determine the range effectively, one can follow a systematic approach. The first step involves identifying the ordered pairs, which in this case are {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}. Following this, the next step is to extract the y-values contained within each pair. After extracting them, one proceeds to list these values, ensuring each output is unique to avoid repetitions. The final stage involves double-checking for completeness, confirming that all y-values from the ordered pairs have been accounted for in the range.

The range serves multiple important functions in understanding mathematical operations. Firstly, it is integral in analyzing function behavior; by knowing the range, one gains insight into the possible outcomes and constraints of the function’s inputs. For example, a limited range indicates that the function cannot produce certain values. Secondly, the range proves beneficial when graphing functions, as it indicates the extent of y-axis values that will appear in the graph. Lastly, the implications of the range extend to real-world applications, representing various constraints or limits—such as in temperature modeling—where the range indicates achievable values within a specific context.

Several common inquiries emerge regarding the range of a function. For instance, many ask what constitutes the range of a set of ordered pairs and how to compute it. The range is simply the collection of y-values present in the ordered pairs. To find this, one must extract y-values and compile them. Understanding the range is crucial for analyzing a function’s behavior and the nature of its potential outputs. Additionally, some may wonder if a function can possess an infinite range; indeed, while certain functions maintain an infinite range, the specific example provided showcases a finite range. Furthermore, the relationship between the range and the domain—where the domain consists of all possible inputs (x-values)—is essential for grasping the overall function mapping.

In conclusion, the range of the function {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)} can be identified as {0, –3, –9, 5, 7}. Analyzing the set of ordered pairs allows for an easy extraction of y-values, thus determining the range. Understanding this aspect is vital for any mathematical discourse as it informs the analysis of a function’s overall behavior, assists in interpreting outputs, and enables a deeper comprehension of the relationships between various elements of the function. Whether engaging with simple functions or more intricate cases, the process for determining the range consistently revolves around the identification of y-values present in the given ordered pairs.