Use the table to answer the question.

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.
1)exponential function
2)absolute value function
3)linear function

Answer 1

To analyze the data provided in the table:

• At 0 seconds, the height is 2 inches.
• At 2 seconds, the height is 4 inches.
• At 4 seconds, the height is 4 inches.
• At 6 seconds, the height is 2 inches.
• At 8 seconds, the height is 0 inches.

Looking at the pattern of the heights:

• The height increases from 2 to 4 inches over the first two seconds.
• It then remains constant at 4 inches for the next two seconds.
• After that, the height decreases to 2 inches at 6 seconds.
• Finally, it decreases further to 0 inches at 8 seconds.

This pattern suggests that the height increases to a maximum (4 inches) and then decreases, which indicates a parabolic shape. However, since we are only considering the options provided:

1. Exponential function: This does not fit the data as the height does not continuously increase or decrease in a multiplicative manner.
2. Absolute value function: This can create a “V” shape, but the dataset doesn't strictly have that pattern.
3. Linear function: This suggests a straight line, which does not represent the change in height accurately, as it does not account for the peaks and valleys observed in the data.

Given these observations, none of the provided options (1, 2, or 3) perfectly fit the data's behavior. However, if we must choose from these options, the closest match to the parabolic pattern would be the absolute value function, as the height first increases, then remains constant, and finally decreases.

So the best option from the provided choices would be:

2) absolute value function.