The graph below displays the wrist circumferences and heights of six students in Alyssa’s classroom.

Question

A graph titled Wrist Circumference versus Height has wrist circumference (centimeters) on the x-axis and height (centimeters) on the y-axis. Points are at (13.8, 151), (14.2, 151), (15.2, 156), (15.6, 159), (16, 162) and (16, 165).

Is the height of these students a function of their wrist circumference?
Yes because as wrist circumference increases height also increases.
Yes because a line can be fit to these data to predict other pairings.
No because the height of 151 cm is paired with two wrist circumferences.
No because the wrist circumference of 16 cm is paired with two heights.

Answer 1

To determine if height is a function of wrist circumference, we need to consider the definition of a function: every input (wrist circumference in this case) must have exactly one output (height).

Looking at the graph data:

• The wrist circumference of 13.8 cm corresponds to a height of 151 cm.
• The wrist circumference of 14.2 cm also corresponds to a height of 151 cm.
• The wrist circumference of 15.2 cm corresponds to the height of 156 cm.
• The wrist circumference of 15.6 cm corresponds to the height of 159 cm.
• The wrist circumference of 16 cm corresponds to two heights: 162 cm and 165 cm.

Since we have a case where the wrist circumference of 16 cm leads to two different heights, it violates the definition of a function. Therefore, height is not determined solely by wrist circumference in this dataset.

The correct answer is: No because the wrist circumference of 16 cm is paired with two heights.