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Which of the following functions best fits the data shown in the scatterplot below?

(1 point)
Responses

y=4x+8
y is equal to 4 to the x th power plus 8

y=20x2+10
y is equal to 20 x squared plus 10

y=100x+2
y is equal to 100 x plus 2

y=2x+5

1 answer

To determine which function best fits the data from a scatterplot, you would typically analyze the shape and trend of the data points.

  • Linear Functions: Functions of the form \(y = mx + b\) (like \(y = 4x + 8\), \(y = 100x + 2\), and \(y = 2x + 5\)) represent a straight line. If the scatterplot shows a linear trend, one of these functions may fit.

  • Exponential Function: The function \(y = 4^x + 8\) represents an exponential growth curve. If the scatterplot shows rapid growth, this might be a fit.

  • Quadratic Function: The function \(y = 20x^2 + 10\) represents a parabolic curve. If the scatterplot resembles a U-shape or an inverted U-shape, this might be the best fit.

Without seeing the actual scatterplot, you would select the function based on the observed trend. If the data points rise and fall in a parabolic shape, then the quadratic function might be the best fit. If they trend upwards in a straight line, a linear function is better. For an exponential trend, you would choose the exponential function.

If you could describe the shape or pattern of the data from the scatterplot, I could help you make a better-informed choice.