The problem states that the number of cups in a stack is a function of the height of the stack in centimeters. We need to sketch a possible graph of this function on a coordinate plane, label the axes, and identify one point on the graph, explaining its meaning in the context of the problem.

1. Problem Description

The problem states that the number of cups in a stack is a function of the height of the stack in centimeters. We need to sketch a possible graph of this function on a coordinate plane, label the axes, and identify one point on the graph, explaining its meaning in the context of the problem.

2. Solution Steps

a. Sketching the graph:

First, we label the axes. Let the x-axis represent the number of cups and the y-axis represent the height of the stack in centimeters.

When there are no cups, the height of the stack is

0. This gives us the point (0, 0).

If we add one cup, there is some height. This will be point (1, h1).

Adding more cups will increase the height, but the rate of increase might decrease if the cups nest well together.

A reasonable graph would be an increasing function, starting at (0,0). It could be linear or slightly concave down as the rate slows with more cups. Let's assume we have cups that are relatively uniform and stack consistently. We'll draw a nearly straight line.

b. Identifying a point on the graph:

Let's consider the point (5, 15). This point suggests that a stack of 5 cups has a height of 15 centimeters.

3. Final Answer

a. The x-axis is labeled "Number of Cups" and the y-axis is labeled "Height (cm)". The graph is a roughly straight line starting at (0,0) and passing through, for example (5, 15).

b. The point (5, 15) means that a stack of 5 cups is 15 centimeters tall.