Question

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

$x$	1	2	3	4	5
$f(x)$	$-4$	$-11$	$-18$	$-25$	$-32$

answer attempt 1 out of 2
this function is because .

Explanation:

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

For \( x = 1 \) to \( x = 2 \): \( -11 - (-4) = -7 \)
For \( x = 2 \) to \( x = 3 \): \( -18 - (-11) = -7 \)
For \( x = 3 \) to \( x = 4 \): \( -25 - (-18) = -7 \)
For \( x = 4 \) to \( x = 5 \): \( -32 - (-25) = -7 \)

Step2: Analyze the pattern of the differences.

The differences between consecutive \( f(x) \) values are all equal (\( -7 \)). In a function, if the first - differences (differences between consecutive outputs) are constant, the function is linear.

Answer:

This function is linear because the difference between consecutive \( f(x) \) values is constant (each difference is \( -7 \)).