Question

answer attempt 1 out of 2 the function is because as x increases, the y values change . the of this function is exactly . x | f(x)
2 | -3
3 | -13
4 | -23
5 | -33

Explanation:

Step1: Check if linear (constant difference)

Calculate differences between consecutive \( f(x) \) values:
\( -13 - (-3) = -10 \), \( -23 - (-13) = -10 \), \( -33 - (-23) = -10 \).
Difference is constant (\(-10\)), so function is linear.

Step2: Find slope (\(m\)) and equation

Slope \( m = \frac{\Delta f(x)}{\Delta x} = \frac{-10}{1} = -10 \).
Use point-slope: \( y - (-3) = -10(x - 2) \) → \( y = -10x + 20 - 3 = -10x + 17 \).
Check: For \( x=2 \), \( -20 + 17 = -3 \) (correct).

Step3: Identify function type and rate

Function is linear (constant rate of change).
Rate of change (slope) is \(-10\).

Answer:

The function is \(\boldsymbol{\text{linear}}\) because as \( x \) increases, the \( y \)-values change by a constant rate. The rate of change of this function is \(\boldsymbol{-10}\).