Question

Which type of function best models the data in the table?

Type of Function

This table shows the relationship between x and y.
x y
2 0.5
5 −1.75
8 −4


(1 point)
Responses

linear
linear

quadratic
quadratic

exponential
exponential

cubic

Answer 1

To determine which type of function best models the data in the table, we can analyze the change in \(y\) values as \(x\) changes. The data points are:

- \( (2, 0.5) \)
- \( (5, -1.75) \)
- \( (8, -4) \)

First, let's check for a linear relationship. In a linear function, the change in \(y\) should be proportional to the change in \(x\):

1. From \(x = 2\) to \(x = 5\):
- Change in \(x\) = \(5 - 2 = 3\)
- Change in \(y\) = \(-1.75 - 0.5 = -2.25\)
- Slope = \(\frac{-2.25}{3} = -0.75\)

2. From \(x = 5\) to \(x = 8\):
- Change in \(x\) = \(8 - 5 = 3\)
- Change in \(y\) = \(-4 - (-1.75) = -2.25\)
- Slope = \(\frac{-2.25}{3} = -0.75\)

The slope remains constant, indicating a linear relationship.

Now let's consider other options such as quadratic or higher degree functions. However, since the slope is consistent, it suggests that the data can be modeled by a linear function.

Given this analysis, the best fitting model for the data is:

**Response: linear**