Question

answer attempt 1 out of 2 the function is because as x increases, the y values change exactly . the of this function is x | f(x)
2 | -28
3 | -31
4 | -34
5 | -37

Explanation:

Step1: Identify Function Type

Check the rate of change between consecutive \( x \) and \( f(x) \). For \( x = 2 \) to \( 3 \): \( \Delta f(x)= -31 - (-28)= -3 \). \( x = 3 \) to \( 4 \): \( -34 - (-31)= -3 \). \( x = 4 \) to \( 5 \): \( -37 - (-34)= -3 \). Constant rate, so linear.

Step2: Determine Rate of Change

The change in \( f(x) \) per unit \( x \) is \( -3 \) (slope \( m = -3 \)).

Step3: Find Equation (Optional, for confirmation)

Using point - slope: \( f(x)-f(2)=m(x - 2) \). \( f(2)= -28 \), so \( f(x)+28=-3(x - 2)\Rightarrow f(x)=-3x - 22 \). The function is linear because \( y \)-values change by a constant rate (slope) of \( -3 \).

Answer:

The function is \(\boldsymbol{\text{linear}}\) because as \( x \) increases, the \( y \)-values change by the \(\boldsymbol{\text{constant rate}}\) of \(\boldsymbol{-3}\) of this function.