Question

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

$x$	1	2	3	4	5
$f(x)$	9	13	17	21	25

answer attempt 1 out of 2
this function is because

Explanation:

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

For \( x = 1 \) to \( x = 2 \): \( 13 - 9 = 4 \)
For \( x = 2 \) to \( x = 3 \): \( 17 - 13 = 4 \)
For \( x = 3 \) to \( x = 4 \): \( 21 - 17 = 4 \)
For \( x = 4 \) to \( x = 5 \): \( 25 - 21 = 4 \)

Step2: Analyze the differences.

The difference between consecutive \( f(x) \) values is constant (4) as \( x \) increases by 1 each time. In a function, if the rate of change (the difference in \( f(x) \) for a unit change in \( x \)) is constant, the function is linear.

Answer:

This function is linear because the difference between consecutive \( f(x) \) values is constant (4) as \( x \) increases by 1, indicating a constant rate of change, which is a characteristic of a linear function.