Question

use the function and graph to answer the questions about existence, limits, and continuity.
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}
does f(-2) exist?
yes
no

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

Answer:

No