Question

answer the questions below to determine what kind of function is depicted in the table below.

x	-2	-1	0	1	2
f(x)	13	11	9	7	5

answer attempt 1 out of 2

this function is because
.

Explanation:

Step1: Calculate the differences between consecutive \( f(x) \) values.

For \( x = -2 \) to \( x = -1 \): \( 11 - 13 = -2 \)
For \( x = -1 \) to \( x = 0 \): \( 9 - 11 = -2 \)
For \( x = 0 \) to \( x = 1 \): \( 7 - 9 = -2 \)
For \( x = 1 \) to \( x = 2 \): \( 5 - 7 = -2 \)

Step2: Analyze the differences.

The difference between consecutive \( f(x) \) values is constant (\( -2 \)) as \( x \) increases by 1 each time. This is the characteristic of a linear function (specifically, a linear function with a constant rate of change, which is the slope in the case of a linear function in the form \( f(x)=mx + b \)).

Answer:

This function is \(\boldsymbol{\text{linear}}\) because the difference between consecutive \( f(x) \) values is constant (the rate of change is constant, with a common difference of \(-2\) as \( x \) increases by \( 1 \) each time).