Question

Which type of function best models the data in the table?
X Y
1 26
4 86
7 146



(1 point)
Responses

Linear
Linear

Quadratic
Quadratic

Cubic
Cubic

Exponential

Answer 1

To determine which type of function best models the data, we can analyze the changes in the \(Y\) values as \(X\) increases.

Let's look at the data provided:

\[
\begin{align*}
X & : 1, 4, 7 \\
Y & : 26, 86, 146 \\
\end{align*}
\]

1. Calculate the differences in \(Y\):
- From \(X = 1\) to \(X = 4\) (going from 26 to 86):
\[
86 - 26 = 60
\]
- From \(X = 4\) to \(X = 7\) (going from 86 to 146):
\[
146 - 86 = 60
\]

The first differences (60, 60) are constant, which suggests the data might be linear.

2. Let's try the second differences:
- Since the first differences are both the same, the second differences are zero. This also confirms a linear relationship.

Given that we have determined that the first differences are constant and the second differences are zero, the best model for this data is a **Linear** function.

**Answer: Linear**