use the function and graph to answer the questions about existence, limits, and continuity.\n…

use the function and graph to answer the questions about existence, limits, and continuity.\n f(x)=\begin{cases}-x - 3, &-5leq xlt - 4\\x + 5, &-4lt xlt - 2\\-\frac{3}{2}x, &-2lt xlt0\\0, &0leq xleq1\\2x - 2, &1lt xlt3\\2, &x = 3\\-2x + 10, &3lt xlt5\\1, &x = 5end{cases}\ndoes f(-2) exist?\nyes\nno

use the function and graph to answer the questions about existence, limits, and continuity.\n f(x)=\begin{cases}-x - 3, &-5leq xlt - 4\\x + 5, &-4lt xlt - 2\\-\frac{3}{2}x, &-2lt xlt0\\0, &0leq xleq1\\2x - 2, &1lt xlt3\\2, &x = 3\\-2x + 10, &3lt xlt5\\1, &x = 5end{cases}\ndoes f(-2) exist?\nyes\nno

Answer

Explanation:

Step1: Check function intervals

The function (f(x)) has intervals. For (x = - 2), the function is not defined at (x=-2) in any of the sub - intervals. The intervals around (x = - 2) are (-4<x<-2) and (-2<x<0), but (x=-2) is not included in either of them.

Answer:

No