## 6.2 Cost per Minute

Explore a linear function or a piecewise function comparing units vs. cost per unit in order to find the total cost.

To change the mode to piecewise or linear, click on the tabs found on the upper right hand corner of the interactive.

For a **linear function**:

To change the cost per unit, drag the purple line on the top graph (up or down).

Investigate the total cost for a given number of units by dragging the white sliders on the bottom graph.

For a **piecewise function**:

To change the cost per unit (top graph), drag the blue or red circles left, right, up, or down.

Investigate the total cost by dragging the white sliders on the bottom graph.

- Why are the segments in the first graph horizontal?
- Why does changing the height of the horizontal segments in the first graph affect the slopes of the line segments in the second graph?
- How can you determine the slopes of the line segments in the second graph (total cost function)?
- Why is the y-intercept zero? Can you think of a pricing scheme for which the y-intercept would not be zero?
- Why is the left part of the total-cost function steeper than the right part? Will it always appear that way? Can you make the right part steeper than the left part?