Use the table to answer the question.

Time (seconds) 0 2 4 6 8
Height (inches) 2 4 4 2 0
Jasmine tracks the flight trajectory of a butterfly, in inches above the ground, over eight seconds. Using the information in the table, determine what type of function would best model her data.

Option #1: exponential function

Option #2: absolute value function

Option #3: linear function

1 answer

To determine what type of function best models the data provided in the table, let's analyze the pattern of the height values over time:

  • At 0 seconds, the height is 2 inches.
  • At 2 seconds, the height increases to 4 inches.
  • At 4 seconds, the height remains at 4 inches.
  • At 6 seconds, the height decreases again to 2 inches.
  • Finally, at 8 seconds, the height reaches 0 inches.

From the above observations, we can see that the height first increases, then stays constant, and subsequently decreases, resembling a "peak" shape. This pattern suggests that the function is not linear, as a linear function would consistently increase or decrease without reversing direction.

Additionally, it does not exhibit the characteristics of an exponential function, which typically shows consistent growth or decay.

The absolute value function, however, can create a shape that rises to a peak and then falls, similar to the height of the butterfly over time as shown in the data.

Based on this analysis, Option #2: absolute value function would be the most appropriate choice to model Jasmine's data.