Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.2 Algebra Techniques for Finding Limits - 14.2 Assess Your Understanding - Page 884: 44

$-3$

General formula for average rate of change from x to y: $\frac{f(y)-f(x)}{y-x}.$ We do what we have to according to the exercise: $$\lim_{x\to -2}\frac{f(x)-f(-2)}{x-(-2)}=\lim_{x\to -2}\frac{(4-3x)-10}{x+2}=\lim_{x\to -2}\frac{-3x-6}{x+2}=\lim_{x\to -2}\frac{-3(x+2)}{x+2}=-3.$$