Final answer:
The range of a function can be determined by graphing the function, which shows the set of all output values. Analytical methods, including calculations, are often more precise than graphical ones, which can be affected by interpretation and scale issues.
Step-by-step explanation:
The range of a function can be determined through multiple methods. One common method is graphing the function. When you graph the function, the range is the set of output values (typically the y-values on the graph), and it can be visually identified as the vertical span of the graph. Another approach is by analyzing the x-intercepts; however, this technique usually gives information about the domain rather than the range. Lastly, consulting a mathematician is always an option, but the standard practices in mathematics allow individuals to determine the range using tools at their disposal without necessarily consulting a professional. While finding the domain involves identifying all possible input values, it doesn't provide direct insight into the range, which concerns the output values.
Moreover, it's important to understand that analytical techniques in determining the range, such as identifying limits and asymptotes or applying the function to its domain's endpoints, can often be more precise than graphical methods. Graphs can be subject to interpretation and scaling issues, whereas analytical methods rely on direct mathematical calculations.