Question

Decide whether the dats Ih the table represents in linear function or an exponential function. Explain how you know.

x y
1 4
2 -5
3 -14
4 -23
5 -32

This table represents a(n) (exponential or linear) function because there is a common (ratio or difference) of (4, -5/4, -9, or 9)

Answer 1

To determine whether the data in the table represents a linear or exponential function, we can analyze how \( y \) changes with respect to \( x \).

First, let's find the differences between successive \( y \) values:

- For \( x = 1 \) to \( x = 2 \):
\[ -5 - 4 = -9 \]
- For \( x = 2 \) to \( x = 3 \):
\[ -14 - (-5) = -9 \]
- For \( x = 3 \) to \( x = 4 \):
\[ -23 - (-14) = -9 \]
- For \( x = 4 \) to \( x = 5 \):
\[ -32 - (-23) = -9 \]

The differences between successive \( y \) values are all equal to \(-9\).

Since the difference between consecutive \( y \) values is constant, this indicates that the relationship between \( x \) and \( y \) is linear.

Therefore, this table represents a **linear function** because there is a common **difference** of \(-9\).