Does the table represent a linear or an exponential function?

Question

x 1 2 3 4
y 8 11 14 17

(1 point)
Responses

Exponential
Exponential

Linear

Answer 1

To determine whether the relationship represented by the table is linear or exponential, we can analyze the changes in the values of \(y\) as \(x\) increases.

The table shows the following pairs:

\[ \begin{array}{|c|c|} \hline x & y \ \hline 1 & 8 \ 2 & 11 \ 3 & 14 \ 4 & 17 \ \hline \end{array} \]

Now, let's find the differences in \(y\) as \(x\) increases:

• From \(x = 1\) to \(x = 2\): \(11 - 8 = 3\)
• From \(x = 2\) to \(x = 3\): \(14 - 11 = 3\)
• From \(x = 3\) to \(x = 4\): \(17 - 14 = 3\)

The differences in \(y\) are constant (3), indicating that the function is linear.

In contrast, an exponential function would show a constant multiplicative rate of change rather than a constant additive rate.

Thus, the answer is Linear.