Below are 4 scatter plots showing the same data for the quantities $f$ and $x$. Each plot uses a different unit for the vertical axis.

Judging from these scatter plots, which type of function would be the best fit for $f(x)$ ?
Choose 1 answer:
(A) Linear
(B) Quadratic
(C) Exponential

D None of the above.

Question

Below are 4 scatter plots showing the same data for the quantities $f$ and $x$. Each plot uses a different unit for the vertical axis.

Judging from these scatter plots, which type of function would be the best fit for $f(x)$ ?
Choose 1 answer:
(A) Linear
(B) Quadratic
(C) Exponential

D None of the above.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Analyze the scatter plot with $f(x)$ as the vertical axis to determine if the data points form a straight line, a parabola, or an exponential curve. ‖ ‖ step 2 ⋮ If the data points in the first plot with $f(x)$ align in a straight line, then the function is linear. If they form a parabola, the function is quadratic. If they align along an exponential curve, the function is exponential. ‖ ‖ step 3 ⋮ Examine the scatter plot with $f(x)^2$ to see if the transformation makes the data points align more closely with a straight line, which would indicate a quadratic function. ‖ ‖ step 4 ⋮ Look at the scatter plot with $\sqrt{f(x)}$ to check if this transformation linearizes the data, suggesting a quadratic function if the points align in a straight line. ‖ ‖ step 5 ⋮ Review the scatter plot with $\log(f(x))$ to determine if this transformation linearizes the data, which would suggest an exponential function if the points align in a straight line. ‖ ‖ step 6 ⋮ Choose the function type that corresponds to the transformation that linearizes the data points the most. ‖ ∻Answer∻ ⚹ The best-fitting function type for $f(x)$ is the one corresponding to the transformation that results in a linear pattern in the scatter plot. Without the actual plots, it is not possible to determine the correct answer. ⚹ ∻Key Concept∻ ⚹Data Fitting with Transformations⚹ ∻Explanation∻ ⚹To determine the best-fitting function type for a set of data points, one can use transformations such as squaring, square rooting, or taking the logarithm of the data and then analyzing the resulting scatter plots for linear patterns. The transformation that linearizes the data indicates the type of function that best fits the original data.⚹◊What mathematical methods can be used to determine the best fitting function for the given scatter plots?⍭ Generate me a similar question◊

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