Question

from unit 5, lesson 1
the number of cups in a stack is a function of the height of the stack in centimeters.
a. sketch a possible graph of the function on the coordinate plane. be sure to label the axes.
b. identify one point on the graph, and explain the meaning of the point in the situation.
algebra 1

Explanation:

Step1: Identify the variables

The independent variable is the height of the stack (x - axis) and the dependent variable is the number of cups (y - axis).

Step2: Consider the nature of the function

Since cups are whole objects, the number of cups changes in discrete steps as the height of the stack increases.

Step3: Interpret a point

For a point \((x,y)\) on the graph, \(x\) represents the height of the stack and \(y\) represents the number of cups in the stack at that height.

Answer:

a.

• On the x - axis, label it "Height of the stack (cm)". On the y - axis, label it "Number of cups". The graph will be a step - like function. When the height is 0, the number of cups is 0. As the height increases in discrete amounts (each cup has a certain height), the number of cups increases in whole numbers. For example, if the height of one cup is \(h\) cm, the graph will have horizontal segments (constant number of cups) until the height reaches a multiple of \(h\), at which point the number of cups jumps up by 1.

b. Let's say the point \((5h,5)\) is on the graph. The meaning of this point is that when the height of the stack of cups is \(5h\) centimeters (where \(h\) is the height of one cup), there are 5 cups in the stack.