Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the range of a function?

1. The set of all possible input values for the function

2. The set of all possible output values (y-values)

3. The slope of the graph of the function

4. The highest and lowest values of the function

The correct answer is: The set of all possible output values (y-values)

The range of a function refers specifically to the set of all possible output values, which are the y-values obtained when you apply the function to its domain (the set of possible input values). When a function is defined, it takes inputs from its domain and produces corresponding outputs. The collection of these outputs constitutes the range. Understanding the range is crucial in various contexts, such as analyzing the behavior of the function, determining limits, and identifying the scope of the outputs for real-world applications. This concept is commonly illustrated through graphs, where the range encompasses all the y-values that the graph touches or approaches. While other concepts such as the domain, slope, and extreme values of the function are important in function analysis, they do not define the range. The domain relates to input values, slope refers to the rate of change of the graph, and the highest and lowest values describe specific aspects of the function but do not capture the entirety of the output values like the range does.