Analyze the scatterplot to explain the most likely transformation necessary to linearize the data. (2 points)

Question

a	The scatterplot resembles a power model, emulating a square root function with a downward curve. Squaring the y-values would linearize the data.
b	The scatterplot resembles an exponential model, emulating a squared function with a downward curve. Squaring the y-values would linearize the data.
c	The scatterplot resembles a power model, emulating a square root function with a downward curve. Taking the square root of the y-values would linearize the data.
d	The scatterplot resembles a power model, emulating a squared function with a downward curve. Exponentiating the y-values to a power of 10 would linearize the data.
e	The scatterplot resembles an exponential model, emulating a squared function with a downward curve. Exponentiating the y-values to a power of 10 would linearize the data.

Answer 1

The answers list the following possible functions:

a) power function. This is y = a•x^b and the words say square root function which would mean b = 1/2

b) exponential function. This seems to be contradictory because an exponential function is y = ab^x while the words discuss it as a squared function y = x² so I would through this answer out based on the conflict.

c) power function. This is y = a•x^b and the words say square root function which would mean b = 1/2 (same as answer a) except the linearization is different.

d) power function. This is y = a•x^b and the words say square root function which would mean b = 1/2 (same as answers a) and c) except the linearization is different.

e) exponential function. This again seems to be contradictory because an exponential function is y = ab^x while the words discuss it as a squared function y = x² so I would through this answer out based on the conflict.

So that means the possible answers are a, c, & d

Consider what the square root function looks like that is discussed in answers a, c, & d. For the simplest square root function y = √x some data points are (0, 0), (1, 1), (4, 2), (9, 3), (16, 4) because we plug in x and take the square root to get y. A linear function that is similar would have the data points (0, 0), (1, 1), (4, 4), (9, 9), (16, 16). What would you need to do the the square root function to turn it into the linear function?