Question

Math

Posted 5 months ago

```
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.
```

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Answer from Sia

Posted 5 months ago

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.

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