Final answer:
Piecewise functions are best suited for relationships between variables that are not continuous, allowing different rules for different intervals. Linear, inverse, or exponential relationships can be captured with simple equations and often plotted as line graphs, but piecewise functions accommodate sudden changes.
Step-by-step explanation:
Piecewise functions are particularly useful when the relationship between variables is not continuous. This is because piecewise functions can be defined with different rules for different intervals of the independent variable, which is ideal for representing situations where there is a sudden change or break in continuity.
On the other hand, relationships such as linear, inverse, and exponential can often be expressed using simple equations without the need for piecewise definitions. A linear relationship can be represented by a simple equation of a line, y=mx+b, while an inverse relationship can be defined by equations like y=k/x, where k is a constant.
An exponential relationship is characterized by a change in the independent variable producing a proportional change in the dependent variable, where the rate of growth increases as the value increases, such as in the growth of bacteria.
A line graph is often the most effective format for illustrating relationships between two variables, especially when both variables are changing, like in time series graphs. However, when the relationship between the variables has breaks or different behaviors in different intervals, a piecewise function's graph would be more appropriate to capture these changes.
Economic models, scientific data, and many other real-world situations often necessitate the use of graphs to visualize data, including piecewise functions when appropriate.
Therefore answer is b) Is not continuous.