Question

Rachel found this rate of change for the scenario represented in the table.

A two column table with six rows. The first column is Time in hours, and has the entries, 4, 5, 6, 7, 8. To the left of this column there are arrows from 4 to 5, 5 to 6, 6 to 7, and 7 to 8 all labeled with plus 1. The second column is Juice in cups, and has the entries, 128, 181, 234, 287, 340. To the right of this column there are arrows from 128 to 181, 181 to 234, and 287 to 340 all labeled with plus 53.

What can you conclude from her work? Check all that apply.

The function is continuous.
Time represents the dependent variable.
The scenario is represented by a linear function, since the rate of change is constant.
As the amount of time continues, there are fewer cups of juice poured per hour.
For every additional hour, 53 cups of juice are poured.

Answer 1

Correct choices:
- The scenario is represented by a linear function, since the rate of change is constant.
- For every additional hour, 53 cups of juice are poured.

Reasoning:
- The juice increases by 53 cups each time the time increases by 1 hour (181−128 = 53, 234−181 = 53, …), so the rate of change is constant (53 cups/hour) — that's a linear relationship.
- You cannot conclude "time represents the dependent variable" (juice depends on time, so time is independent).
- You cannot conclude "the function is continuous" just from the table of discrete values (continuity would follow if you assume the linear model extends between the times, but the table alone doesn’t force continuity).
- "Fewer cups of juice poured per hour" is false because the rate is constant, not decreasing.