Hal, Zelda, Maya, and Jason each recorded the height and age of five classmates. They used the data to create the tables below.

Question

4 tables. A 2-column table titled Hal's results has 5 rows. Column 1 is labeled Age with entries 15, 14, 16, 12, 13. Column 2 is labeled Height (inches) with entries 55, 61, 69, 55, 59. A 2-column table titled Zelda's results has 5 rows. Column 1 is labeled Age with entries 12, 14, 16, 14, 12. Column 2 is labeled Height (inches) with entries 60, 61, 62, 63, 64. A 2-column table titled Maya's results has 5 rows. Column 1 is labeled Age with entries 12, 12, 12, 12, 12. Column 2 is labeled Height (inches) with entries 56, 62, 64, 58, 67. A 2-column table titled Jason's results has 5 rows. Column 1 is labeled Age with entries 12, 13, 12, 14, 15. Column 2 is labeled Height (inches) with entries 50, 54, 57, 60, 68.

In which student’s data can height be considered a function of age?
Hal
Zelda
Maya
Jason

Answer 1

To determine if height can be considered a function of age for each student's data, we need to check if the same age corresponds to a unique height value. In other words, for each age recorded, there should be only one height associated with it.

1. Hal's results:

   • Age 12: Height 55
   • Age 13: Height 59
   • Age 14: Height 61
   • Age 15: Height 55
   • Age 16: Height 69

   No age value is repeated, so height can be considered a function of age.

2. Zelda's results:

   • Age 12: Height 60
   • Age 14: Height 61 (twice)
   • Age 16: Height 62
   • Age 16: Height 63
   • Age 12: Height 64

   Age 12 corresponds to two different heights (60 and 64), and age 14 also corresponds to two different heights (61 and 63). Therefore, height cannot be considered a function of age.

3. Maya's results:

   • Age 12: Height 56
   • Age 12: Height 62
   • Age 12: Height 64
   • Age 12: Height 58
   • Age 12: Height 67

   This is the same age (12) corresponding to five different heights. Thus, height cannot be considered a function of age.

4. Jason's results:

   • Age 12: Height 50 (twice)
   • Age 13: Height 54
   • Age 14: Height 60
   • Age 15: Height 68

   Age 12 corresponds to two different heights (50). Thus, height cannot be considered a function of age.

Based on this analysis, only Hal's data allows height to be considered a function of age.