A graph titled Scenario A, Swimmer's Distance to time has time (seconds) on the x-axis, and distance (meters) on the y-axis. Points are at (5, 10), (10, 18), (15, 28), (20, 36), and (25, 47). A 2-column table with 5 rows titled Scenario B, 100 meters time to swimmer's height. Column 1 is labeled height t (inches) with entries 67, 69, 70, 70, 72. Column 2 is labeled Time (seconds) with entries 52.34, 55.76, 54.6, 53.11, 54.03.

Question

Compare these two scenarios.

Which scenario, A or B, represents a function?

Answer 1

To determine which scenario represents a function, we need to analyze the relationship between the input and output in each case.

Scenario A: Swimmer's Distance to Time

• In Scenario A, time (in seconds) is on the x-axis and distance (in meters) is on the y-axis. The points provided are:
  • (5, 10)
  • (10, 18)
  • (15, 28)
  • (20, 36)
  • (25, 47)

Each time value (x-coordinate) maps to exactly one distance value (y-coordinate). Since no x-value is repeated with different y-values, this scenario satisfies the definition of a function.

Scenario B: 100 Meters Time to Swimmer's Height

• In Scenario B, the height (in inches) is in Column 1, and the time (in seconds) is in Column 2. The entries are:
  • 67 inches → 52.34 seconds
  • 69 inches → 55.76 seconds
  • 70 inches → 54.6 seconds
  • 70 inches → 53.11 seconds
  • 72 inches → 54.03 seconds

Here, we notice that the height of 70 inches corresponds to two different time values (54.6 seconds and 53.11 seconds). Because this height (70 inches) maps to two different times, this scenario does not satisfy the definition of a function.

Conclusion:

Scenario A represents a function, whereas Scenario B does not represent a function because a single input (height of 70 inches) corresponds to multiple outputs (different times).