Final answer:
To determine whether a relationship is a function, use the vertical line test. The domain consists of all possible inputs, the range includes all outputs. The independent variable is plotted on the x-axis, while the dependent is on the y-axis, and regression analysis can predict relationships between them.
Step-by-step explanation:
To determine if a relationship is a function, one must look at each input (domain) and output (range). The domain is the set of all possible input values, while the range is the set of all possible output values. A relation is a function if every input has exactly one output, which can be tested using the vertical line test. When a vertical line intersects the graph at more than one point, the relation is not a function.
An independent variable is one that stands alone and isn't changed by the other variables you are trying to measure. Conversely, a dependent variable is something that depends on other factors. In a scatter plot, the independent variable is typically plotted on the x-axis, while the dependent variable is plotted on the y-axis.
To analyze the relationship between two variables, one can use regression analysis to find a line of best fit, which is represented by the equation y = a + bx. The correlation coefficient, ranging from -1 to 1, measures the strength and direction of the linear relationship between variables. A correlation coefficient close to 1 or -1 indicates a strong relationship, while a value near 0 suggests a weak relationship. If the correlation coefficient suggests a significant linear relationship, we can use the line of best fit to make predictions.