Final answer:
To determine if a relation is a function, assess whether each input has a single corresponding output, using steps such as identifying variables, plotting data, and calculating the line of best fit and correlation coefficient. If every input has one output, then the relation is a function.
Step-by-step explanation:
To determine if a relation is a function, you need to assess whether each input, which comes from the domain, has a corresponding single output in the range. The rule is that every input must be associated with exactly one output, not multiple outputs. If this criterion is met, then the relation can be considered a function. This is a foundational concept in mathematics, particularly when modeling relationships between variables.
Steps to Determine if a Relation is a Function:
- Decide which variable should be the independent variable and which should be the dependent variable. The independent variable is the one that is being changed or controlled in the experiment, while the dependent variable is the one that is being tested and measured.
- Draw a scatter plot of the ordered pairs. A scatter plot can give a visual representation of the data and help indicate whether there is a function-like relationship where each input corresponds to only one output.
- Use regression to find the least-squares line, putting the equation in the form ý = a + bx. This statistical method helps to define a linear function that best fits the data points in a scatter plot.
- Find the correlation coefficient to determine the strength of the relationship. A significant strong correlation would indicate a well-defined function.
If after following these steps, you find that each input (x-value) in your set of ordered pairs corresponds to exactly one output (y-value), your relation is a function.