Answer
Option D is the answer.
y = 0.19 √[120 (x + 2.29)]
Step-by-step explanation
We are asked to find the function that fits the data in the table.
To do this, we will need to check some of these functions by putting the values in the table in it and seeing if they fit
Option A
y = 0.29 √[110 (x + 1.95)]
when x = -2, y = 1
y = 0.29 √[110 (-2 + 1.95)]
y = 0.29 √[110 (-0.05)]
y = 0.29 √[-5.5]
Since there isn't a real number square root for negative numbers, there is no value for y when x = -2
Option A cannot be the answer.
Option B
y = 0.25 √[130 (x + 2.5)]
when x = -2, y = 1
y = 0.25 √[130 (-2 + 2.5)]
y = 0.25 √[130 (0.5)]
y = 0.25 √[65]
y = 0.25 (8.1)
y = 2
2 ≠ 1
Option B is not the answer.
Option C
y = 0.37 √[115 (x - 2.14)]
when x = -2, y = 1
y = 0.37 √[115 (-2 - 2.14)]
y = 0.37 √[115 (-4.14)]
y = 0.37 √[-476.1]
Since there isn't a real number square root for negative numbers, there is no value for y when x = -2
Option C cannot be the answer.
Option D
y = 0.19 √[120 (x + 2.29)]
when x = -2, y = 1
y = 0.19 √[120 (-2 + 2.29)]
y = 0.19 √[120 (0.29)]
y = 0.19 √[34.8]
y = 0.19 (5.9)
y = 1.1 = 1
Since this is the only one that even the first value on the table fits, this has to be the only option that fits the data.
We can check the rest of the data for this too, but since all the other options failed the first test, it is clear that this option is the correct answer.
Hope this Helps!!!