Question

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

$x$	0	1	2	3	4

answer attempt 1 out of 2

this function is because

Explanation:

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

For \( x = 0 \) to \( x = 1 \): \( -16 - (-10) = -6 \)
For \( x = 1 \) to \( x = 2 \): \( -22 - (-16) = -6 \)
For \( x = 2 \) to \( x = 3 \): \( -28 - (-22) = -6 \)
For \( x = 3 \) to \( x = 4 \): \( -34 - (-28) = -6 \)

Step2: Analyze the differences.

The difference between consecutive \( f(x) \) values is constant (\( -6 \)). In a function, if the first - differences (differences between consecutive outputs) are constant, the function is linear. The general form of a linear function is \( f(x)=mx + b \), where \( m \) is the slope (here \( m=-6 \)) and \( b \) is the y - intercept (when \( x = 0 \), \( f(0)=-10 \), so \( b=-10 \)).

Answer:

This function is a linear function because the difference between consecutive \( f(x) \) values (the first - differences) is constant (\( - 6\)).