Question

answer attempt 1 out of 2 the function is linear because as x increases, the y values change additively multiplicatively. the common difference/slope of this function is
f(x) -3 -13 -23 -33

Explanation:

Step1: Analyze function type

A linear function has a constant rate of change. For the given \( f(x) \) values: \(-3\), \(-13\), \(-23\), \(-33\), we check the difference between consecutive terms.

Step2: Calculate the change

\(-13 - (-3) = -10\), \(-23 - (-13) = -10\), \(-33 - (-23) = -10\). The change is constant (additive), so the function changes additively. The common difference (slope for linear) is \(-10\).

Answer:

The function is linear because as \( x \) increases, the \( y \)-values change additively. The common difference/slope of this function is \(-10\). (For the first dropdown: additively; for the slope: \(-10\))